# STA301 Subjective Questions Short Notes

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    Pie                 Pie Chart consists of a circle which is divided into two or more mars in
Chart                accordance with the number of distinct classes that we have in our data.
:

    Statistical                      Statistical Inference is an estimate or prediction or some other
Inference :                       generalization about a Population based on information contained
in a sample.

    Statistics :                    Statistics is that science which enables to draw conclusions about
various phenomena one the basis of real data collected on sample
basis.

    Sample :                       Sample is that part of the Population from which information is
collected.

    What is                    Order: Arrangement of objects in ascending or descending way is
meant                       known as order.
by
order?. :
Ordinal            It includes the characteristic of a nominal scale and in addition has the property of
Scale :            ordering or ranking of measurments e.g the performance of students can be rated
as excellent,good or poor.

Interval           A measurment scale possessing a constant interval size but not true zero point is
Scale :            called an Interval Scale.

Ratio Scale It is a special kind of an interval scale in which the scale of measurment has a true
:           zero point as its origin.
Median :           Median of a set of values arranged in ascending or descending order of magnitude
is defined as middle value if the number of values is odd and mean of two middle
values if the number of values is even.Median is a value at or below which 50% of
data lie.

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Average :          A single value which intended to represent a distribution or a set of data as a
whole is called an average. It is more or less a central value around which the
observations tend to cluster so it is called measure of central tendency. Since
measure of central tendency indicate the location of the distribution on X axis so it
is also called measure of location.

Mean        The mean deviation is defined as the arithmetic mean of the deviations measured
Deviation : either from the mean or from the median, all deviations being counted as positive.

Chebshev's Chebshev's Theorem states that "For any number K greater than one at least 1-
Theorm :   1/k2 of the data values fall with in K standard deviations of the mean i.e. within
the interval.

Moments : Moments are the arithmetic means of the powers to which the deviations are
raised.
Kurtosis :         kurtosis is the degree of peakness of a distribution usually taken relative to a
normal distribution.

Correlation Correlation is a measure of the strength or the degree of relationship between two
:           random variables. OR Interdependence of two variables is called correlation.

Venn               A diagram that is understood to represent sets by circular regions, parts of circular
Diagram :          regions or their complements with respect to a rectangle representing the space S
is called a Venn diagram. The Venn diagrams are used to represent sets and
subsets in a pictorial way and to verify the relationship among sets and subsets.

Mutually           Two events are said to be mutually exclusive events if and only if they can not
Exclusive          both occur together at the same time. OR Two events are said to be mutually
Event :            exclusive events if the occurrence of one event discard the occurrence of other
event.

Independent Two events A and B in the same sample space S, are defined to be independent
events :    (or statistically independent) if the probability that one event occurs, is not
affected by whether the other event has or has not occured.
Random             A numerical quantity whose value is determined by the outcome of a random

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variable :         experiment is called a random variable.

Distribution The function which gives the probability of the event that X takes a value less than
Function : or equal TO a specified value x is called a distribution function and is also called
the cumulative distribution function.

Cumulative The function which gives the probability of the event that X takes a value less than
Distribution or equal TO a specified value x is called a cumulative distribution function and is
Function : also called the distribution function.

Sampling           A sampling frame is a complete list of all the elements in the population.
Frame :

Sampling           The sampling error is the difference between the the sample statistic and the
Error :            population parameter.
Probability Probability samples are those in which following the sampling plan each unit in
Samples : the poplation has a known probability of being included in the sample.

Non         Non probability samples are those in which the sample elements are the arbitrarily
probability selected by the sampler because in this judgment the elements thus chosen will
samples :   most effectively represent the Population.

Frequency          A frequency polygon is obtained by plotting the class frequencies against the mid-
Polygon :          points of the classes, and connecting the points so obtained by straight line
segments.

Variable :         A measurable quantity which can vary from one individual or object to another is
called a variable.

Constant :         A quantity which can assume only one value is called a constan
Event. :           the possible outcomes of an experiment is known as event.

Data. :            A well defined collection of objects is known as data.

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Mode :             The mode is a value which occures most frequently in a set of data i.e. it indicates
the most common result

Box and            A Box and Whisker plot provides a graphical representation of data through its
Whisker            five number summary.
plot :

The five  A five number summary consists of X0, Q1, median, Q3, and Xm. It enables us to
number    find the shape of the distribution without drawing a graph.
summary :
EXHAUSTIVE Two or more than two mutually exclusive events are said to be exhaustive
EVENTS :   events when their union constitute the entire sample space

Equally       Two events A and B are said to be equally likely when one event is as likely to
likely events occur as other
:

Probability Probability is defined as the ratio of favorable cases over equally likely cases.
:

Table :            Table is a systematic arrangement of data into vertical columns and horizontal
rows.

Tabulation The process of arranging data into rows and columns is called tabulation.
:
Classification The process of arranging data in classes or categories according to some common
:              characteristics present in the data is called classification.

Class Mark The class mark or mid point is that value which divides a class into two equall
or Mid     parts.
Point :

Mid Poin or The mid point or class mark is that value which divides a class into two equal
Class Mark parts.
:

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Measure of A single value which intended to represent a distribution or a set of data as a
location : whole is called an average. It is more or less a central value around which the
observations tend to cluster so it is called measure of central tendency. Since
measure of central tendency indicate the location of the distribution on X axis so it
is also called measure of location.

The Semi- The quartile deviation or the Semi-interquartile Range is defined as half of the
interquartile difference between the first and third quartiles.
Range :
The          The coefficient of variation expresses the standard deviation as the percentage of
coefficient the arithmetic mean.
of variation
:

Disjoint Set Two sets A and B are said to be disjoint Sets if they have no elements in common.
:

DISTRIBUTION The distribution function of a random variable X, denoted by F(x), is defined
FUNCTION: : by F(x) = P(X < x). The function F(x) gives the probability of the event that
X takes a value LESS THAN OR EQUAL TO a specified value x. The
distribution function is abbreviated to d.f. and is also called the cumulative
distribution function (cdf) as it is the cumulative probability function of the
random variable X from the smallest value up to a specific value x.

Experimental An experimental design is a set of rules or a plan to collect the data relevant to
design: :    the problem under investigation in such a way as to provide the basis for valid
and objective inferences about the stated problem. The plan usually consists of
collection of the treatments, specification of experimental layout, allocation of
treatments.

Experimental An experimental unit is the basic unit to which the experiment is performed. It is
Unit: :      the basic unit to which the treatment is applied and in which the variable under
investigation is measured and analyzed.

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Randomized These designs are those in which treatments are applied to experimental units
Deigns; :  randomly and conclusions are supported by the statistical results.

Basic      Randomization Replication Local Control
Randomized
Designs: :

Randomization: It is a random process of assigning treatments to the experimental unit. The
:              random process implies that every possible allocation of treatments has the
same probability.

Replication: The second principle of an experimental design is replication which is the
:            repetition of the basic experiment. It is a complete run of all the treatments to be
tested in the experiment.

Local              It is used to bring all extraneous sources of variations under control. For this
Control: :         purpose we use Local Control, a term referring to the amount of balancing,
blocking and grouping of the experimental units.
Complete   In this design treatments are applied to the experimental units completely at
Randomized random, that is randomization is done without any restrictions. Design is
Designs :  completely flexible, any number of treatments and any number of units per
treatments can be applied.

ANOVA :            Analysis of variance is defined as the procedure by means of which the total
variability of the set of data measured by total sum of square is partitioned into
components that measure different sources of variations. The procedure thus
permits the decomposition of the total SS into to the component SS which are
corresponding to the real and suspected sources of variations.

Randomized Randomized complete block Design (RCB) is a design in which • Experimental
complete   material is divided into groups or blocks in such a manner that experimental units
block      within a particular block are relatively homogeneous. • Each block contains
Design     complete set of treatments i.e. it constitutes a replication of treatments. •
(RCB): :   Treatments are assigned at random to the experimental units with in each block
which means the randomization is restricted with blocks.

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Latin              LS design is an arrangement of k treatments in a k*k square, where the treatments
Square             are grouped in blocks in two directions, the direction being orthogonal to each
Design: :          other and to the treatments, and where the treatments appear once and only once in
each in each direction. It should be noted that in Latin square design, the number
of rows, the number of columns and number of treatments must be equal

Critical           The value that separates the critical region from the acceptance region, is called
Value :            the critical value(s).
Level of     Level of significance of a test is the probability used as a standard for rejecting
significance null hypothesis Ho when Ho is assumed to be true. The level of significance acts
:            as a basis for determining the critical region of the test.

statistics 2 : Statistics is a science of facts and figures.

Deciles :          Deciles are those nine quantities that divide the distribution into ten equall parts.

Percentiles : Percentiles are those ninety nine quantities that divide the distribution into
hundred equall parts

Arithmetic Arithmetic Mean is a value obtained by dividing the sum of the observations by
Mean :     their numbers.
Geometric          The Geometric Mean G, of a set of n positive values is defined as the positive nth
Mean :             root of their product.

Absolute     An absolute measure of dispersion is one that measures the dispersion in terms of
Measure of the same units, or in the square of units as the units of the data.
Dispersion :

Dispersion : The variability that exists between data set.

Relative     A Relative Measure of Dispersion is one that measures the dispersion in terms of a
Measure of ratio, coefficient or percentage and is independent of the units of measurement.
Dispersion :

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Range :            The range is defined as the difference between the maximum and minimum values
of a data set.
Quartile    The quartile deviation is defined as half of the difference between the first and
Deviation : third quartiles.

Set :              A set is any well defined collection or list of distinct objects.

standard           The degree of scatter of the observed values about the regression line measured by
error of           what is called standard deviation of regression or standard error of estimate.
estimate :

Class of           A set of sets is called a class.
Sets :

Primary            The data published or used by an organization which originally collected them are
Data :             called primary data thus the primary data are thr first hand information collected,
Secondary          The data published or used by an organization other than the one which
Data :             origninally collected them are known as secondary data.

Harmonic           Harmonic mean is defined as the reciprocal of the arithmetic mean of the
Mean :             reciprocals of the values.

Quartiles : Quartiles are those three quantities that divide the distribution into four equal
parts.

Quantiles : Collectively the quartiles, the deciles,percentiles and other values obtained by
equall sub-division of the data are called quantiles.

Index              An Index Number is a statistical measure which shows changes in a variable or
Number :           group of related variables with respect to time, geographic location or other
characteristics such as income, profession etc.
Standard    Standard Deviation is defined as the positive square root of the mean of the
Deviation : squared deviations of the values from their mean.

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Variance :         Variance is defined as the square of the standard deviation.

Regression : Dependence of one variable on the other variable is called regression. OR
Estimation or prediction of one variable on the basis of other variable is called
regression.

Random     An experiment which produces different results even though it is repeated a large
Experiment number of times under essentially similar conditions is called a random
:          experiment.

Sub Set :          A set that consists of some elements of an other set is called a subset of that set.
Non-               Such errors which are not attributable to sampling but arise in the process of data
Sampling           collection even if a complete count is carried out.
Error :

Skewness : Skewness is the lack of symmetry in a distribution around some central value
(mean,median or mode).It is thus the degree of a symmetry.

Permutation an arrangement of all or some of a set of objects in a definite order is called
:           permutation.

Universal          All sets are subsets of one particular set called universal set.
Set :

Sample             The set or collection of all possible outcomes of an experiment is called the
Space :            sample space.
Conditional The probability of the occurence of an event A when it is known that some other
Probability event B has already occured is called the conditional probability.
:

Degrees of         Degrees of freedom can be defined as the number of observations in the sample
freedom :          minus the number of population parameters that are estimated from the sample
data (from those observations

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P value :          The p-value is a property of the data, and it indicates “how improbable” the
obtained result really is.

Test               A statistic (i.e. a function of sample data not containing any parameter), which
Statistic :        provides a basis for testing a null hypothesis, is called a test statistics.

Addition           A probability law used to compute the probability of a union of two events,
law :              denoted A and B. It is P(AÈB)=P(A)+P(B)-P(AÇB). For mutually exclusive
events, because P(AÇB)=0, it reduces to P(AÈB)=P(A)+P(B).
Alternative The hypothesis concluded to be true if the null hypothesis is rejected.
hypothesis :

ANOVA              A table used to summarize the analysis of variance computations and results. It
table :            contains columns showing the source of variation, the sum of squares, the degrees
of freedom, the mean square, and the F values.

Bayes'             A method used to compute posterior probabilities.
theorem :

Binomial     A probability distribution showing the probability of x successes in n trials of a
probability binomial experiment.
distribution
:

Binomial    The function used to compute probabilities in a binomial experiment.
probability
function :
Blocking :         The process of using the same or similar experimental units for all treatments. The
purpose of blocking is to remove a source of variation from the error term and
hence provide a more powerful test for a difference in population or treatment
means.

Box plot :         A graphical summary of data. A box, drawn from the first to the third quartiles,
shows the location of the middle 50% of the data. Dashed lines, called whiskers,

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extending from the ends of the box show the location of data values greater than
the third quartile and data values less than the first quartile. The locations of any
outliers are also noted.

Central            A theorem that enables one to use the normal probability distribution to
limit              approximate the sampling distribution of the sample mean and sample proportion
theorem :          whenever the sample size is large.

Consistency A property of a point estimator that is present whenever larger sample sizes tend
:           to provide point estimates closer to the population parameter

Histogram : A graphical presentation of a frequency distribution, relative frequency
distribution, or percent frequency distribution of quantitative data constructed by
placing the class intervals on the horizontal axis and the frequencies on the vertical
axis.
Null         The hypothesis tentatively assumed true in the hypothesis testing procedure. or A
hypothesis : null hypothesis, generally denoted by the symbol H0, is any hypothesis which is to
be tested for possible rejection or nullification under the assumption that it is true.

Normal       A continuous probability distribution. Its probability density function is bell
probability shaped and determined by its mean m and standard deviation s.
distribution
:

Observation The set of measurements obtained for a single element.
:

Ogive :            A graph of a cumulative distribution.

One-tailed         A hypothesis test in which rejection of the null hypothesis occurs for values of the
test :             test statistic in one tail of the sampling distribution. or The entire rejection region
lies in only one of the two tails, either in the right tail or in the left tai, of the
sampling distribution of the test-statistic, is called a one-tailed test or one-sided
test.
Parameter : numerical characteristic of a population, such as a population mean, a population

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standard deviation, a population proportion, and so on.

Point              A single numerical value used as an estimate of a population parameter.
estimate :

Point       The sample statistic that provides the point estimate of the population parameter.
estimator :

Poisson      A probability distribution showing the probability of x occurrences of an event
probability over a specified interval of time or space.
distribution
:

Poisson     The function used to compute Poisson probabilities.
probability
function :
Population A numerical value used as a summary measure for a population of data (e.g., the
parameter : population mean, the population variance, and the population standard deviation).

Posterior     Revised probabilities of events based on additional information.
probabilities
:

Power              A graph of the probability of rejecting H0 for all possible values of the population
curve :            parameter not satisfying the null hypothesis. The power curve provides the
probability of correctly rejecting the null hypothesis.

Power :            The probability of correctly rejecting H0 when it is false.

Probability A function used to compute probabilities for a continuous random variable. The
density     area under the graph of a probability density function over an interval represents
function : probability.
Probability A function, denoted by f(x), that provides the probability that x assumes a
function : particular value for a discrete random variable.

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Qualitative Data that are labels or names used to identify an attribute of each element.
data :      Qualitative data may be nonnumeric or numeric.

Qualitative A variable with qualitative data.
variable :

Quantitative Data that indicate how much or how many of something. Quantitative data are
data :       always numeric.

t            A family of probability distributions that can be used to develop interval estimates
Distribution of a population mean whenever the population standard deviation is unknown and
:            the population has a normal or near-normal probability distribution.
population :

Treatment : Different levels of a factor.

Tree               A graphical representation helpful in identifying the sample points of an
diagram :          experiment involving multiple steps.

Two-tailed A hypothesis test in which rejection of the null hypothesis occurs for values of the
test :     test statistic in either tail of the sampling distribution.

Type I             The error of rejecting H0 when it is true.
error :
Type II            The error of accepting H0 when it is false.
error - :

Unbiasedness A property of a point estimator when the expected value of the point estimator is
:            equal to the population parameter it estimates.

Union of           The event containing all sample points that are in A, in B, or in both. The union is
events A           denoted AÈB.

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and B :

Types of     Systematic Designs Randomized design
Experimental
Designs: :

Systematic These designs are those in which treatments are applied to the experimental units
Designs: : by some systematic manner that is choice of the experimenter
Acceptance         All possible values which a test-statistic may assume can be divided into two
and                mutually exclusive groups: One group consisting of values which appear to be
rejection          consistent with the null hypothesis (i.e. values which appear to support the null
region: :          hypothesis), and the other having values which lead to the rejection of the null
hypothesis. The first group is called the acceptance region and the second set of
values is known as the rejection region for a test

Type I             When we perform a hypothesis test, we derive evidence from the sample in the
error: :           form of a test statistics. There is a possibility that sample may lead us to make a
wrong decision. We may reject the hypothesis when it is in fact true. This type of
error is called an error of first kind or type I-error. The probability of committing a
type I error is denoted by α. Thus α is the probability of rejecting null hypothesis
Ho when Ho true.

Type II            When we perform a hypothesis test, we derive evidence from the sample in the
error: :           form of a test statistics. There is a possibility that sample may lead us to make a
wrong decision. We may accept the hypothesis when it is in fact false. This type of
error is called an error of second kind or a Type II error. The probability of
committing a type II error is denoted by β. Thus β is the probability of accepting
null hypothesis Ho when Ho false.

Class              The point in each class that is halfway between the lower and upper class limits.
midpoint :

Complement The event consisting of all sample points that are not in A.
of event A :
Dependent The variable that is being predicted or explained. It is denoted by y.
variable :

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Descriptive Tabular, graphical, and numerical methods used to summarize data.
statistics :

Dot plot :         A simple graphical summary of data with each observation represented by a dot
placed above a horizontal axis that shows the range of values for the observations.

Discrete           A random variable that may assume either a finite number of values or an infinite
random             sequence of values.
variable :

Empirical          A rule that states the percentages of items that are within one, two, and three
rule :             standard deviations from the mean for mound-shaped, or bell-shaped,
distributions.
Experiment A process that generates well-defined outcomes.
:

Binomial   A probability experiment having the following four properties: consists of n
experiment identical trials, two outcomes (success and failure) are possible on each trial,
:          probability of success does not change from trial to trail, and the trials are
independent.

Factorial  An experimental design that allows statistical conclusions about two or more
experiment factors.
:

Five-     An exploratory data analysis technique that uses the following five numbers to
number    summarize the data set: smallest value, first quartile, median, third quartile, and
summary : largest value.

Frame :            A list of the sampling units for a study. The sample is drawn by selecting units
from the frame
Frequency A tabular summary of data showing the number (or frequency) of items in each of
distribution several non-overlapping classes.
:

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Grouped            Data available in class intervals as summarized by a frequency distribution.
data :             Individual values of the original data are not available.

Independent The variable that is doing the predicting or explaining. It is denoted by x.
variable :

Intersection The event containing all sample points that are in both A and B. The intersection
of A and B : is denoted AÇB.

Joint       The probability of two events both occurring; that is, the probability of the
probability intersection of two events.
:
Judgment           A nonprobabilistic method of sampling whereby element selection is based on the
sampling :         judgment of the person doing the study.

Interquartile A measure of variability, defined to be the difference between the third and first
range (IQR) quartiles.
:

Least              The method used to develop the estimated regression equation. It minimizes the
squares            sum of squared residuals (the deviations between the observed values of the
method :           dependent variable, yi, and the estimated values of the dependent variable, yi)

Regression The equation that describes how the mean or expected value of the dependent
equation : variable is related to the independent variable.

Rejection          The range of values that will lead to the rejection of a null hypothesis.
region :
Replication The number of times each experimental condition is repeated in an experiment.
:

Residual :         The difference between the observed value of the dependent variable and the value
predicted using the estimated regression equation.

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Sample             An element of the sample space. A sample point represents an experimental
point :            outcome.

Sample             A numerical value used as a summary measure for a sample (e.g., the sample
statistic :        mean, the sample variance, and the sample standard deviation). The value of the
sample statistic is used to estimate the value of the population parameter.

Sampled      The population from which the sample is taken.
population :
Sampling           The units selected for sampling. A sampling unit may include several elements.
unit :

Sampling Once an element has been included in the sample, it is returned to the population.
with        A previously selected element can be selected again and therefore may appear in
replacement the sample more than once.
:

Sampling Once an element has been included in the sample, it is removed from the
without     population and cannot be selected a second time.
replacement
:

Scatter            A graph of bivariate data in which the independent variable is on the horizontal
diagram :          axis and the dependent variable is on the vertical axis.

Simple       Regression analysis involving one independent variable and one dependent
linear       variable in which the relationship between the variables is approximated by a
regression : straight line.
Simple             Finite population: a sample selected such that each possible sample of size n has
random             the same probability of being selected. Infinite population: a sample selected such
sampling :         that each element comes from the same population and the elements are selected
independently.

Standard           The standard deviation of a point estimator.

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error :

Stem-and- An exploratory data analysis technique that simultaneously rank orders
leaf display quantitative data and provides insight about the shape of the distribution.
:

Stratified         A probability sampling method in which the population is first divided into strata
random             and a simple random sample is then taken from each stratum.
sampling :

Hypergeometric The function used to compute the probability of x successes in n trials when
probability    the trials are dependent.
function :
Multiplication A probability law used to compute the probability of an intersection of two
law :          events, denoted A and B. It is P(AÇB)=P(A)P(B|A) or P(AÇB)= P(B)P(A|B).
For independent events it reduces to P(AÇB)=P(A)P(B).

Goodness of A statistical test conducted to determine whether to reject a hypothesized
fit test :  probability distribution for a population.

Sampling A probability distribution consisting of all possible values of a sample statistic.
distribution
:
Mean
 The mean of the sampling distribution (of the mean) is the mean of
the population from which the scores were sampled.
 Therefore, if a population has a mean, μ, then the sampling
distribution of the mean is also μ.
 The symbol  X is used to refer to the mean of the sampling
distribution of the mean.
    Therefore, the formula for the mean of the sampling distribution of the
mean can be written as:

X  

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Variance
    The variance of the sampling distribution of the mean is computed as
follows:

2
X 
2

N

    That is, the variance of the sampling distribution of the mean is the
population variance divided by N.
    Thus, the larger the sample size, the smaller the variance of the
sampling distribution of the mean.

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Table of Standard Normal Probabilities, P(Z < z)

z     0.00       0.01       0.02       0.03       0.04      0.05       0.06       0.07       0.08       0.09

0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

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1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890

2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993

3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995

3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

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3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998

3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

z     0.00       0.01       0.02       0.03       0.04      0.05       0.06       0.07       0.08       0.09

It is a standard normal cumulative table. Let suppose you want to fine the value of 95% confidence
interval for mean, than calculating Z-value is making problem, it can be found as

(1-  )% confidence interval means               (1  95)%  5%  0.05

Z / 2  Z0.05/ 2  Z0.025  1  0.025  0.975

See 0.975 in the above table, values against it in row wise 1.9 and column wise 0.06 (highlighted with
red color), we add these to get Z-value,

Z = 1.9 +0.06 = 1.96

Similarly, if you want to fine the value of 98% C.I the Z-value calculated as

(1-100)% confidence interval means                 (1  98)%  2%  0.0.02

Z / 2  Z0.02 / 2  Z0.01  1  0.010  0.990

See 0.990 in the above table that is 2.33 (highlighted with green color).

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