# Statistic Descriptive by U3B7jkAM

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```									         Chapter 4.
Describing Data: Displaying
And Exploring Data

http://statisticdescriptive.wordpress.com/

Displaying & Exploring     Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   1
Data
Stem And Leaf Displays
   Stem and leaf display:
- a statistical technique to present a set of
data.
- Each numerical value is divided into two
parts.
- The leading digit becomes the stem, and
the trailing digit the leaf.
- The stems are located along the vertical axis,
and the leaf values are stacked against each
other along the horizontal axis.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   2
Data
Example Page 102:
Data:
96, 93, 88, 117,127, 95, 113, 96, 108, 94,
148, 156, 139, 142, 94, 107, 125, 155, 155,
………………………………………………......
…...................................................................
124, 138

The smallest number is 88
The largest number is 156

Displaying & Exploring           Ir.Muhril Ardiansyah,M.Sc.,Ph.D.      3
Data
Steam               Leaf
8                   89
9                   3445667
10                  334678
11                  122337789
12                  00455577
13                  2456899
14                  238
15                  556

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   4
Data
Other Measures Of Dispersion

   The standard deviation is the most
widely used measures of dispersion.
   Others are:
- quartiles.
- deciles.
- percentiles.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   5
Data
Other Measures Of Dispersion
(continued)

   Quartiles:
divide a set of observations into four
equal parts.
   Deciles:
divide a set of observations into 10 equal
parts.
   Percentiles:
divide a set of observations into 100
equal parts.
Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   6
Data
Other Measures Of Dispersion
(continued)

   Percentiles:
- location of a percentile
(equation 4-1, Page 107)
LP = (n + 1) (P/100)
Lp = the location of a desired percentile
n = the number of observation
P = the desired percentile

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   7
Data
   If we want to find the 33rd percentile we
want to find L33

   If we want to find median, we want to
find L50

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   8
Data
Example Page 107
   The Data:
2038, 1758, 1721, 1637, 2097, 2047, 2205, 1787, 2287,
1940, 2311, 2054, 2406, 1471, 1460
n = 15

Sort the data from the smallest to the largest:

1460, 1471, 1637, 1721, 1758, 1787, 1940, 2038, 2047,
2054, 2097, 2205, 2287, 2311, 2406

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   9
Data
Example Page 107 (continued)
   The median = L50 = Second Quartile
L50 = (15+1)(50/100) = 8
The position number 8 is 2038

   L25 = First Quartile
L25 = (15+1)(25/100)= 4
The position number 4 is 1721

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   10
Data
Example Page 107 (continued)
   L75 = Third Quartile
L75 = (15+1)(75/100) = 12
The position number 12 is 2205

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   11
Data
Example Page 108
   The Data:
43, 61, 75, 91, 101, 104
n=6
L25 = (6+1)(25/100) = 1.75
First value is 43, second value is 61.
The distance first value and second value is
(61- 43) = 18.
We need move 0.75 of the distance between
first and second value: 0.75 (18) = 13.5, so
L25 = 43 + 13.5 = 56.5

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   12
Data
Box Plots
   A graphical display based on quartiles.
   Needed:
1. The minimum value.
2. The first quartile.
3. The median.
4. The third quartile.
5. The maximum value.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   13
Data
Example Page 110
Alexander’s Pizza offers free delivery of its
pizza within 15 miles. Alex, the owner,
wants some information on the time it
takes for delivery.
- How long does a typical delivery take?

- Within what range of times will most
deliveries be completed?

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   14
Data
Example Page 110 (continued)
For a sample of 20 deliveries, he determined
the following information:
Minimum value is 13 minutes.
Q1 (the first quartile) is 15 minutes.
Median is 18 minutes.
Q3 (the third quartile) is 22 minutes.
Maximum value is 30 minutes.

Develop a box plot for the delivery times.
What conclusions can you make about delivery times?

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   15
Data
Example Page 110 (continued)
Step 1: Create an appropriate scale along the horizontal
axis.
Step 2: Draw a box that starts at Q1 and ends at Q3.
Step 3: Inside the box, place a vertical line to represent the
median.
Step 4: Extend the horizontal lines from the box out to the
minimum value and the maximum value.

Look figure page 111
The box plot shows that the middle 50 percent of the
deliveries take between 15 minutes and 22 minutes.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   16
Data
Skewness
    The shape
    Four shapes:
1. Symmetric.
2. Positively skewed (skewed to the right).
3. Negatively skewed (skewed to the left).
4. Bimodal.

Chart 4-1 Page 114

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   17
Data
Skewness (continued)
     To calculate skewness:
- Pearson’s coefficient of skewness
Equation 4-1 Page 114
sk = {3(X bar – Median)} / s
s = standard deviation of sample

**Skewness range: -3 up to 3
**Value near -3, indicates considerable negative
skewness.
**Value near 3, indicates considerable positive
skewness.
**Value of 0, indicates symmetrical and no skewness.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   18
Data
Example Page 115
The sample data (n=15):
0.09, 0.13, 0.41, 0.51, 1.12, 1.20, 1.49, 3.18,
3.50, 6.36, 7.83, 8.92, 10.13, 12.99, 16.40
- Compute the mean.
- Compute the median.
- Compute the standard deviation.
- Find the coefficient of skewness using
Pearson’s estimate.
- What is your conclusion regarding the shape of
the distribution?

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   19
Data
Example Page 115 (continued)
X bar is 74.26/15 = 4.95
The middle value is 3.18

S = root of {S(X – X bar)2 / (n-1)} = 5.22

Sk = {3(4.95-3.18)}/5.22 = 1.017
Indicates there is moderate positive
skewness.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   20
Data
Describing The relationship Between
Two Variables
   Using “ A Scatter Diagram”:
- need two variables.
- One variable along the horizontal axis
(X-axis).
- The other variable along the vertical axis
(Y-axis).

Chart 4-1 page 119

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   21
Data
Chapter 4.
Describing Data: Displaying
And Exploring Data

http://statisticdescriptive.wordpress.com/

Displaying & Exploring     Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   22
Data
Homework
No. 31 Page 124-125.

Displaying & Exploring   Ir.Muhril Ardiansyah,M.Sc.,Ph.D.   23
Data

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