ComputerIntegrated

assessment

Computer integrated assessmentComputer integrated assessment

Tabulating and graphing of test data

Tabulating and graphing of test dataTabulating and graphing of test data

Tabulating of data

Graphing of data

Tabulating of dataTabulating of data

Reason for tabulating

Listing

Simple frequency distribution

Tabulating & Graphing

Grouped frequency distribution

Reason for tabulating dataReason for tabulating data

To make sense of data.

36 63 51 43 9354 48 84 36 4557 45 48 96 6658 72 81 30 2745 51 47 63 88

Can you make sense of this data?

Tabulating

One way to tabulate data.

List data in an ascending sequence.

List data in a descending sequence.

Listing of dataListing of data

96 72 54 48 4397 66 54 47 3698 63 51 45 3699 63 51 45 3081 57 48 45 27

27 45 48 57 8130 45 51 63 8436 45 51 63 8836 47 54 66 9343 48 54 72 96

Ascending sequenceDescending sequence

Tabulating

Simple frequency distributionSimple frequency distribution

XX ff XX ff XX ff XX ff XX ff XX ff

9696 11 8484 11 7272 11 6060 00 4848 22 3636 22

9595 00 8383 00 7171 00 5959 00 4747 11 3535 00

9494 00 8282 00 7070 00 5858 00 4646 00 3434 00

9393 11 8181 11 6969 00 5757 11 4545 33 3333 00

9292 00 8080 00 6868 00 5656 00 4444 00 3232 00

9191 00 7979 00 6767 00 5555 00 4343 11 3131 00

9090 00 7878 00 6666 11 5454 22 4242 00 3030 11

8989 00 7777 00 6565 00 5353 00 4141 00 2929 00

8888 11 7676 00 6464 00 5252 00 4040 00 2828 00

8787 00 7575 00 6363 22 5151 22 3939 00 2727 11

8686 00 7474 00 6262 00 5050 00 3838 00 -- --

8585 00 7373 00 6161 00 4949 00 3737 00 -- --

Tabulating

Grouped frequency distributionGrouped frequency distribution

Step 1: Determine the range of scores R = highest score - lowest score R = 96 – 27 = 69

Step 2: Determine number of intervalsStep 3: Divide the range by the number of intervals and round to an odd number

i = R = 69/10 = 6,9 (7) number of intervals

Step 4: Construct the interval columnStep 5: Construct the frequency column

Tabulating

Grouped frequency distributionGrouped frequency distribution

Lower limit Lower limit (LL)(LL)

Upper limit Upper limit (UP)(UP)

112112 118118

105105 111111

9898 104104

9191 9797

8484 9090

7777 8383

7070 7676

6363 6969

5656 6262

4949 5555

4242 4848

3535 4141

2828 3434

2121 2727

1414 2020

77 1313

Highest score;eliminate intervals

above

Lowest score;eliminate intervals

below

IntervalsIntervals

91 – 9791 – 97

84 – 9084 – 90

77 – 8377 – 83

70 – 7670 – 76

63 - 6963 - 69

56 – 6256 – 62

49 – 5549 – 55

42 – 4842 – 48

35 – 4135 – 41

28 – 3428 – 34

21 - 2721 - 27

Lower limit is amultiple of theinterval width.

Upper limit isone point lessthan the lower

limit of the nextinterval.

Interval column

Step 4: Construct the interval column

Tabulating

27 45 48 57 8130 45 51 63 8436 45 51 63 8836 47 54 66 9343 48 54 72 96

Interval Tally f

91 - 97

84 - 90

77 - 83

70 - 76

63 - 69

56 - 62

49 - 55

42 - 48

35 - 41

28 - 34

21 - 27

2

2

1

1

3

1

4

7

2

1

1

Frequency with Excel

Step 5: Construct the frequency column

Grouped frequency distribution

Graphing of test dataGraphing of test data

The histogram

The frequency polygon

The cumulative frequency polygon

Tabulating & Graphing

The histogramThe histogram

The histogram is based on the grouped frequency distribution.

Interval f

91 - 97 2

84 - 90 2

77 - 83 1

70 - 76 1

63 - 69 3

56 - 62 1

49 - 55 4

42 - 48 7

35 - 41 2

28 - 34 1

21 - 27 1

0

1

2

3

4

5

6

7

21 - 27 28 - 34 35 - 41 42 - 48 49 - 55 56 - 62 63 - 69 70 - 76 77 - 83 84 - 90 91 - 97

f

Interval

Histogram of test scoresGrouped frequencydistribution

Graphing

The frequency polygonThe frequency polygon

The graph is straight line connecting the midpoint of each interval.

0

1

2

3

4

5

6

7

8

24 31 38 45 52 59 66 73 80 87 94

Midpoint

Frequency polygon of test scoresGrouped frequency distribution

Interval Midpoint f

91 - 97 94 2

84 - 90 87 2

77 - 83 80 1

70 - 76 73 1

63 - 69 66 3

56 - 62 59 1

49 - 55 52 4

42 - 48 45 7

35 - 41 38 2

28 - 34 31 1

21 - 27 24 1

Midpoint (MP) = LL + UL

2

f

Graphing

The cumulative frequency polygonThe cumulative frequency polygon

The cumulative frequency polygon is based on the cumulative frequency distribution.

Interval Midpoint f cf

91 - 97 94 2 25

84 - 90 87 2 23

77 - 83 80 1 21

70 - 76 73 1 20

63 - 69 66 3 19

56 - 62 59 1 16

49 - 55 52 4 15

42 - 48 45 7 11

35 - 41 38 2 4

28 - 34 31 1 2

21 - 27 24 1 1

Cumulative frequencydistribution

0

5

10

15

20

25

30

27 34 41 48 55 62 69 76 83 90 97

Cumulative frequency polygon (OGIVE)

Upper level

cf

GraphingAlternative tutorial