# Bsic Statistics Presentation

W
Shared by:
Categories
Tags
-
Stats
views:
18
posted:
8/31/2012
language:
English
pages:
32
Document Sample

```							INTRODUCTION TO
STATISTICS

Md. Mortuza Ahmmed
Applications of Statistics

Agriculture
Marketing Research
Education
Medicine
Variable
Qualitative
Variable

Independe                    Dependent
nt variable                   variable

Discrete                    Continuous
variable                     variable

Quantitative
Variable
Scales of Measurement

Nominal   Ordinal
scale     Scale

Ratio    Interval
scale      scale
FREQUENCY TABLE
Rating of                            Relative
Tally marks Frequency
Drink                              Frequency

P            IIII        05      05 / 25 = 0.20

G         IIII IIII II   12      12 / 25 = 0.48

E           IIII III     08      08 / 25 = 0.32

Total                     25               1.00
SIMPLE BAR DIAGRAM
160
150
140

120
100
100

80

60                       56

40
25
20

0
Muslim    Hindu   Christians   Others
COMPONENT BAR DIAGRAM

300

250

200
Section D
Section C
150
Section B
100                           Section A

50

0
Male   Female
MULTIPLE BAR DIAGRAM

100
90
80
70
60                       Section A
50                       Section B
40                       Section C
Section D
30
20
10
0
Male   Female
PIE CHART

Religion of students
Muslim    Hindu     Christians   Others

8%

15%
46%

31%
LINE GRAPH

Share price of BEXIMCO
7000
6400
6000

5600
5000
5000                                          4500
4000

3000
3000
2000

1000

0
July       August     September   October   November
HISTOGRAM

20
18
16
14
12
10
8
6
4
2
0
BAR DIAGRAM VS. HISTOGRAM

Histogram            Bar diagram

Area gives frequency Height gives frequency

each others          to each others

Constructed for       Constructed for
quantitative data     qualitative data
STEM AND LEAF PLOT

Stem    Leaf
1    1479
2    13479
3    1379
4    1347
5    1349
6    1347
SCATTER DIAGRAM

300

250

200
Supply

150

100

50

0
0    5   10    15     20   25   30
Price
COMPARISON AMONG THE GRAPHS

Shows percent of total     Use only discrete data
Pie chart
for each category
Can compare to normal     Use only continuous data
Histogram
curve
Compare 2 or 3 data sets    Use only discrete data
Bar diagram
easily
Compare 2 or 3 data sets Use only continuous data
Line graph
easily
Shows a trend in the data Use only continuous data
Scatter plot
relationship

Stem and Leaf    Handle extremely large     Not visually appealing

Plot                data sets
MEASURES OF CENTRAL TENDENCY

A measure of central tendency is a single
value that attempts to describe a set of data
by identifying the central position within
that set of data.

 Arithmeticmean (AM)
 Geometric mean (GM)

 Harmonic mean (HM)

 Median

 Mode
ARITHMETIC MEAN

It is equal to the sum of all the values in the
data set divided by the number of values in
the data set.
PROBLEMS
   Find the average of the values 5, 9, 12, 4, 5, 14,
19, 16, 3, 5, 7.

   The mean weight of three dogs is 38
pounds.   One of the dogs weighs 46
pounds.  The other two dogs, Eddie and
Tommy, have the same weight. Find Tommy’s
weight.

   On her first 5 math tests, Zany received
scores 72, 86, 92, 63, and 77. What test score
she must earn on her sixth test so that her
average for all 6 tests will be 80?
AFFECT OF EXTREME VALUES ON AM

Staff   1   2 3 4   5   6   7   8   9 10

Salary 15 18 16 14 15 15 12 17 90 95
CALCULATION OF AM FOR GROUPED DATA

x              f       f.x
0             05       00
1             10       10
2             05       10
3             10       30
4             05       20
10             02       20
Total        N = 37      90
AM     =   90 / 37   =    2.43
MEDIAN

1   3   2
MEDIAN = 2

1   2   3

1   4   3   2
MEDIAN = (2 + 3) / 2
= 2.5
1   2   3   4
MODE
WHEN TO USE THE MEAN, MEDIAN
AND MODE

Best measure of central
Type of Variable
tendency
Nominal                    Mode

Ordinal                    Median

Interval/Ratio (not
Mean
skewed)

Interval/Ratio (skewed)           Median
WHEN WE ADD OR MULTIPLY EACH
VALUE BY SAME AMOUNT

Data             Mean Mode Median
Original     6, 7, 8, 10, 12, 14,   12.2   14   13
data Set       14, 15, 16, 20

Add 3 to     9, 10, 11, 13, 15,     15.2   17   16
each       17, 17, 18, 19, 23
value
Multiply 2   12, 14, 16, 20, 24,    24.4   28   26
to each     28, 28, 30, 32, 40
value
MEAN, MEDIAN AND MODE FOR
SERIES DATA

For a series 1, 2, 3 ….n,
mean = median = mode
= (n + 1) / 2

So, for a series 1, 2, 3 ….100,
mean = median = mode
= (100 + 1) / 2 = 50.5
GEOMETRIC MEAN
HARMONIC MEAN
AM X HM = (GM) 2

For any 2 numbers              AM X HM
a and b,
= (a + b) / 2 . 2ab /
AM = (a + b) / 2                        (a + b)

GM = (ab) ^ ½              = ab

= (GM) 2
HM = 2 / (1 / a + 1 / b)
= 2ab / (a + b)
EXAMPLE
For any two numbers, AM = 10 and
GM = 8. Find out the numbers.

(ab)^ ½ = 08               (a - b)2 = (a + b)2 – 4ab

ab = 64                            = (20)2 – 4 .64
= 144
(a + b) / 2 = 10
a + b = 20 . . . . .(1)     => a - b = 12 . . . .(2)

Solving (1) and (2) (a, b) = (16, 4)
EXAMPLE

For any two numbers, GM = 4√3 and HM = 6.
Find out AM and the numbers.
AM           √ab = 4√3    (a - b)2
= (GM)2/   HM       =>ab = 48       = (a + b)2 – 4ab
= (4√3) 2 / 6                       = (16)2 – 4 . 48
=8              (a + b) / 2 = 8
= 64

=> a + b = 16 …(1) a - b = 8 ...(2)

Solving (1) & (2) (a, b) = (12, 4)
CRITERIA FOR GOOD MEASURES OF CENTRAL
TENDENCY

Clearly defined

Based on all observations

Easily calculated

Less affected by extreme values

Capable of further algebraic
treatment
AM ≥ GM ≥ HM
For any two numbers a & b (√a - √b) 2 ≥ 0

AM = (a + b) / 2          a + b – 2(ab)^1/2 ≥ 0

GM = (ab)^1/2             a + b    ≥ 2(ab)^1/2
HM = 2 / (1 / a + 1 / b) (a + b) / 2 ≥ (ab)^1/2
= 2ab / (a + b)       => AM    ≥ GM

Multiplying both sides by 2(ab)^1/2 / (a + b)
(ab)^1/2 ≥ 2ab / (a + b)
GM ≥ HM

So, AM ≥ GM ≥ HM

```
Related docs
Other docs by MortuzaAhmmed
Introduction to Statistics Presentation