Statistical Display of Data: Tables, Graphs and Charts · Statistical Display of Data: Tables, Graphs and Charts . ... Table 2 Marks obtained by 100 students of the ... The following

Centre for Distance Education, IAE, University of Ghana, Legon

Unit

4

Statistical Display of Data: Tables,

Graphs and Charts

UGRC 120 Numeracy Skills Unit 4 Statistical Display of Data

Centre for Distance Education, IAE, University of Ghana, Legon 23

Activity 1.1

1. Give examples of four types of raw data you would collect from your

town or locality and identify whether they are categorical or numerical.

In the case of a numerical example, say whether they are discrete or

continuous.

(a)……………………………………………………………………..

(b)……………………………………………………………………..

(c)……………………………………………………………………..

(d)……………………………………………………………..………

SAMPLE FREQUENCY DISTRIBUTION TABLE 1

Table 1 Faculty Classification by a sample of 100 students of the

University of Ghana, Legon

Faculty # of Students (f)

Arts 25

Social Studies 38

Science 20

Engineering Sciences 5

Agricultural Science 10

Total = N 100


Table 2 Marks obtained by 100 students of the University of Ghana,

Legon in UGRC 120.

Marks # of Students (f)

20 – 29 5

30 – 39 9



40 – 49 19

50 – 59 25

60 – 69 20

70 – 79 12

80 – 89 10

Total = N 100


The first three classes of Table 4 may be obtained by tallying as follows:

Marks Tally # of Students (f)

20 – 29 //// 5

30 – 39 //// //// 9

40 – 49 //// //// //// //// 19

Activity 1.2

Develop a table of class boundaries or exact limits of the data in Table

1.2.

Marks obtained by 100 students of the University of Ghana, Legon in

UGRC 120

Marks Class Boundaries No. of Students (f)

20 – 29 5

30 – 39 9

40 – 49 19

50 – 59 25

60 – 69 20

70 – 79 12

80 – 89 10

Total = N 100



Activity 1.3

What is the size of the class interval for Table 2? ...............................

Activity 1.4

Develop a table of class midpoints for Table 2

Marks obtained by 100 students of the University of Ghana, Legon in

UGRC 120

Marks # of Students (f) Class Midpoints (x)

20 – 29 5

30 – 39 9

40 – 49 19

50 – 59 25

60 – 69 20

70 – 79 12

80 – 89 10

Total = N 100

Example 1.1 Obtain a stem-and-leaf display for the data below:

16 17 17 18 18 18 19 19 19 20

20 21 22 22 25 27 32 38 42 45

A cursory look at the data indicates that the values are in tens, twenties, thirties and

forties. We will therefore suggest the stems to be the fist digits of the numbers and

the last digits constitute the leaves. We therefore have:

Stem Leaf

1

2

3

4

6 7 7 8 8 8 9 9 9

0 0 1 2 2 5 7

2 8

2 5

Activity 1.5

Develop a stem-and-leaf display for each of the following sets of data. In

each case tell us your definition of the stem and the leaf:



(a) 10.5 , 11. 1 , 11. 2 , 11. 3 , 11. 5 , 12.0 , 12.2 , 12. 3 , 15.7 , 16.2

(b) 120 , 123 , 98 , 99 , 110 , 157 , 143 , 152 , 135 , 149.

Example 1.2

The following are the grades of 50 students in an examination:

13 47 27 55 41 58 35 58 48 53 58 22 55 32 45 48 54

78 66 58 42 35 18 57 30 72 57 81 33 63 54 79 47 64

36 45 51 24 79 26 33 60 18 68 35 20 68 36 60 55

Use a C.I = 10

The lowest value is 13 and the highest is 82. We will consider class

intervals: 10 – 19 , 20 – 29 , 30 – 39 , etc. We therefore, construct the

frequency table as follows:

Class Tally # of cases (f)

10 – 19

20 – 29

30 – 39

40 – 49

50 – 59

60 – 69

70 – 79

80 - 89

///

////

//// ////

//// ////

//// //// //

//// //

////

/

3

5

9

9

12

7

4

1

Total Frequency N = 50



Using Technology

Excel is a spreadsheet which is a software application that comes together

with every computer. Excel has the capability of analyzing data even for

larger sets of data.

Microsoft Excel Terms

When you use Microsoft Excel, you place the data you have collected in

worksheets.

The intersections of the columns and rows of worksheets form boxes

called cells.

If you want to refer to a group of cells that forms a contiguous rectangular

area, you can use a cell range.

Worksheets exist inside a workbook, a collection of worksheets and other

types of sheets, including chart sheets that help visualize data.

Figure 4.1 is an illustration of the Microsoft Worksheet when Excel is opened

on your computer.

Figure 3.1: Microsoft Worksheet



To be able to perform basic statistical analyses that we shall be discussing

in Excel, you have to install the Excel Analysis Tool Pack.

Installation of the Analysis Tool Pack

Step 1:

Open Excel. Click on the

Office button and click on

Excel Options as indicated

in the Figure.

Step 2:

Select Add-Ins and click

OK as indicated in the

Figure.



Step 3:

Make sure „Add-ins‟ is

selected in the Manage:

dialogue box and click

Go… as indicated in the

Figure.

Step 4:

Select „Analysis ToolPak‟ and

„Analysis ToolPak – VBA‟ in the

Add-Ins available: dialogue box and

click OK as indicated in the Figure.

Step 5:

When the Analysis ToolPak Add-In has been installed, click on Data, the last Menu bar shows Data

Analysis. You are now ready to explore the wide variety of statistical analysis that Excel offers.



Example 1.3

Use the data in Example 3.2 to construct a frequency table in Excel.

Enter the data in the worksheet in one column as indicated below:

The bins are the upper end points (or upper boundaries of the intervals).

Step 1:

Click on „Data‟ , then „Data

Analysis‟ in the task pane located at

the uppermost parts of the worksheet.

Select Histogram in the „Data

Analysis‟ dialogue box and click OK

as indicated in the Figure.



Step 2:

Input the cell range of the data by

placing the cursor in the „Input

Range: box and clicking and

holding to select the cells

containing the marks.

Also input the cell range of the

Bins in the „Bin Range:‟ box.

Select „New Worksheet Ply:‟ to

store the result in a new worksheet

or select „Output Range:‟ and

click any cell within the same

worksheet to store the result there.

Click on OK.

Step 3:

Delete the last row and change „Bins‟

to „Class Intervals‟. Change the first

column values appropriately to show

the class intervals.



Multi-Dimensional Tables

When we present data to show more than one characteristic or groups of

items, then we refer to it as Multi-dimensional tables. We present an

illustration of a multi-dimensional table as an example.

Example 1.4

The table below is the result of a survey into cinema attendance habits of

adult factory workers:

This is the ensuing Frequency

distribution.



Activity 1.6

In a` survey of 10, 048 persons, of whom 2, 703 were children under 16

years of age, 605 retired men and 2, 212 housewives, the following

information was obtained. Of those above age 16, there were 2, 720 males

16 and under 60, and 2, 931 females of this age group.

There were 227 males between 60 and 65 and 482 males above 65 and

270 and 515 females in these age ranges respectively.

Construct tables showing the distribution of the distribution of the sample

by work status and the adult population by age and sex. Use percentages

to help in making comparisons. Give you comment on the data.



Example 4.1

Draw a bar chart for the data in Table 1.1

Table 1.1 Faculty Classification by a sample of 100 students of the

University of Ghana, Legon

Faculty # of Students (f)

Arts 25

Social Studies 38

Science 20

Engineering Sciences 5

Agricultural Science 10

Total = N 100



Example 1.4

Draw a pie chart for the data in Table 1.1



Example 1.5 Draw a multiple bar chart for the data in Table 3.2:



Activity 4.1

Use the multi-dimensional table you found in Activity 3.1 to draw a multiple bar

chart.

Example 1.6

Draw a composite bar chart for the data in Table 3.2:

Activity 1.8

Use the multi-dimensional table you found in Activity 3.1 to draw a composite bar

chart.



Example 1.7

Draw a histogram for the data in Example 3.1:



Activity 1.9

Collect data on the ages of 50 students in this class. Organize these data

into a frequency distribution using a class interval size of 10. Draw a

histogram and a frequency polygon for these data.

Frequency Distribution of Examination Scores with

Cumulative Frequency

Example 1.8

Marks obtained by 100 students of the University of Ghana, Legon in UGRC 120

Class

interval

Exact Class

Limits

No. of

Students (f)

Class

Midpoint (x)

CF

Less than

CF

More than

20 – 29 19.5 – 29.5 5 24.5 5 100

30 – 39 29.5 – 39.5 9 34.5 14 95

40 – 49 39.5 – 49.5 19 44.5 33 86

50 – 59 49.5 – 59.5 25 54.5 58 67

60 – 69 59.5 – 69.5 20 64.5 78 42

70 – 79 69.5 – 79.5 12 74.5 90 22

80 – 89 79.5 – 89.5 10 84.5 100 10

Total = N 100

The “less than” cumulative frequency is computed based on the upper

class boundaries/exact limits and the “more than” cumulative frequency is

computed based on the lower class boundaries/exact limits.

This indicates that 14 students scored less 39.5, 33 students scored less

than 49.5, 86 students scored more than 39.5, and 67 students scored more

than 49.5.

Activity 1.10 Explain the difference between the less than and the more than

cumulative frequencies

A graph showing the cumulative frequency “less than” or “more than” any

exact limit is called a cumulative frequency polygon or ogive.



For example from the graph of the cumulative frequency, about 20

students have marks of 60 and more. This is done by drawing a line

perpendicular to the horizontal axis at (100% - 20%) = 80% and extend

the line till it intersects the “more than” curve. At this point of intersection

a line is drawn perpendicular to the vertical axis to intersect the vertical

axis. At this point on the vertical axis the value is seen to be

approximately 63.5 marks.

Activity 1.11 Draw a cumulative frequency distribution of ages of students on the

data you obtained in Activity 5.1

Activity 1.12 In each of the following pairs of charts presented, identify the problem and discuss

among yourselves in groups of five.

CHART 1



CHART 2

‘CHART 3



CHART 4

Assignment 4

1. A recent survey showed that the typical American car owner spends GH¢2,

950 per year on operating expenses. Below is a breakdown of the various

expenditure items. Draw an appropriate chart to portray the data and

summarize your findings in a brief report.



Expenditure Item Amount (in GH¢)

Fuel

Interest on car loan

Repairs

Insurance and license

Depreciation

603

279

930

646

492

Total 2,950

2. The Ministry of Health reported that in the year 2007, the distribution of

Ghanaian cancer patients by age was as follows:

Draw a pie chart to represent the data.

3. The Registrar of the University of Ghana has 16 late applications of the

Matured Entrance Examinations (MEE) for admission into the humanities

programme in the university next academic year. The composite MEE scores

of these applicants were:

27 27 27 28 27 25 25 28

26 28 26 28 31 30 26 26

The MEE scores are to be organized into a frequency distribution.

(a) How many classes would you recommend?

(b) What class intervals would you suggest?

(c) What lower limit would you recommend for the first class?

(d) Organize the scores into a frequency distribution and determine the

relative frequency distribution.

(e) Comment on the shape of the frequency distribution.

Age Group 0 – 19 20 – 39 40 – 59 60+

Percentage of Patients 12.2 13.6 33.1 41.1



4. ECOBANK is studying the number of times their Automatic Teller Machine

(ATM), located at Legon Campus, is used each day. The following is the

number of times it was used during each of the last 30 days. Develop a stem-

and-leaf display for the data. Summarize the data on the number of times the

ATM was used: How many times was the ATM used on a typical day? What

are the largest and the smallest number of times the ATM was used? Around

what values did the number of times the ATM was used tend to cluster?

83 64 84 76 84 54 75 59 70 61

63 80 84 73 68 52 65 90 52 77

95 36 78 61 59 84 95 47 87 60

5. A large retailer is studying the lead time (elapsed time between when an order

is placed and when it is filled) for a sample of recent orders. The lead times are

reported in days:

Lead Time (days) Frequency

0 up to 5

5 up to 10

10 up to 15

15 up to 20

20 up to 25

6

7

12

8

7

(a) How many orders were studied?

(b) What is the midpoint of the first class?

(c) Draw a histogram for the data.

(d) Draw a frequency polygon for the data.

(e) Interpret the lead times using the two charts.

(f) How many orders were filled in less than 10 days? In less than 15

days?

(g) Convert the frequency distribution into a less-than cumulative

frequency distribution.

(h) Develop a less-than cumulative frequency polygon.

(i) About 60 percent of the orders were filled in less than how many days?

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Statistical Display of Data: Tables, Graphs and Charts · Statistical Display of Data: Tables, Graphs and Charts . ... Table 2 Marks obtained by 100 students of the ... The following