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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