measures of central tendency and variability for grouped data
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GROUPED DATAMeasures of Variability
LEARNING OBJECTIVE
At the end of the period, the students
should be able to calculate the
measures of variability of grouped
data.
Height of 45 Students from Grade 8 in cm
Finding the mean, median and mode.
Class tally f Xm fXm LB UB <cf >cf
191-196 I 1 193.5 193.5 190.5 196.5 45 1
185-190 IIIII-IIIII-I 11 187.5 2062.5 184.5 190.5 44 12
179-184 IIIII 5 181.5 907.5 178.5 184.5 33 17
173-178 IIIII-II 7 175.5 1228.5 172.5 178.5 28 24
167-172 IIIII-III 8 169.5 1356 166.5 172.5 21 32
161-166 IIIII-IIIII 10 163.5 1635 160.5 166.5 13 42
155-160 III 3 157.5 472.5 154.5 160.5 3 45
Learning Objective: The students should be able to calculate the measures of central tendency of grouped data.
Height of 45 Students from Grade 8 in cm
Finding the mean, median and mode.
Class Tally f Xm fXm LB UB <cf >cf
191-196 I 1 193.5 193.5 190.5 196.5 45 1
185-190 IIIII-IIIII-I 11 187.5 2062.5 184.5 190.5 44 12
179-184 IIIII 5 181.5 907.5 178.5 184.5 33 17
173-178 IIIII-II 7 175.5 1228.5 172.5 178.5 28 24
167-172 IIIII-III 8 169.5 1356 166.5 172.5 21 32
161-166 IIIII-IIIII 10 163.5 1635 160.5 166.5 13 42
155-160 III 3 157.5 472.5 154.5 160.5 3 45
Learning Objective: The students should be able to calculate the measures of central tendency of grouped data.
Height of 45 Students from Grade 8 in cm
Finding the mean, median and mode.
Class tally f Xm fXm LB UB <cf >cf
191-196 I 1 193.5 193.5 190.5 196.5 45 1
185-190 IIIII-IIIII-I 11 187.5 2062.5 184.5 190.5 44 12
179-184 IIIII 5 181.5 907.5 178.5 184.5 33 17
173-178 IIIII-II 7 175.5 1228.5 172.5 178.5 28 24
167-172 IIIII-III 8 169.5 1356 166.5 172.5 21 32
161-166 IIIII-IIIII 10 163.5 1635 160.5 166.5 13 42
155-160 III 3 157.5 472.5 154.5 160.5 3 45
Learning Objective: The students should be able to organize data in a frequency distribution table.
Normal Distribution/Normal Curve
Bell-shaped curve
symmetrical
Learning Objective: The students should be able to illustrate the measures of variability of a statistical data.
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5
185-190 11 187.5
179-184 5 181.5
173-178 7 175.5
167-172 8 169.5
161-166 10 163.5
155-160 3 157.5
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93
185-190 11 187.5 12.93
179-184 5 181.5 6.93
173-178 7 175.5 0.93
167-172 8 169.5 -5.07
161-166 10 163.5 -11.07
155-160 3 157.5 -17.07
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93 358.3449
185-190 11 187.5 12.93 167.1849
179-184 5 181.5 6.93 48.0249
173-178 7 175.5 0.93 0.8649
167-172 8 169.5 -5.07 25.7049
161-166 10 163.5 -11.07 122.5449
155-160 3 157.5 -17.07 291.3849
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93 358.3449 358.3449
185-190 11 187.5 12.93 167.1849 1839.0339
179-184 5 181.5 6.93 48.0249 240.1245
173-178 7 175.5 0.93 0.8649 6.0543
167-172 8 169.5 -5.07 25.7049 205.6392
161-166 10 163.5 -11.07 122.5449 1225.449
155-160 3 157.5 -17.07 291.3849 874.1547
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93 358.3449 358.3449
185-190 11 187.5 12.93 167.1849 1839.0339
179-184 5 181.5 6.93 48.0249 240.1245
173-178 7 175.5 0.93 0.8649 6.0543
167-172 8 169.5 -5.07 25.7049 205.6392
161-166 10 163.5 -11.07 122.5449 1225.449
155-160 3 157.5 -17.07 291.3849 874.1547
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93 358.3449 358.3449
185-190 11 187.5 12.93 167.1849 1839.0339
179-184 5 181.5 6.93 48.0249 240.1245
173-178 7 175.5 0.93 0.8649 6.0543
167-172 8 169.5 -5.07 25.7049 205.6392
161-166 10 163.5 -11.07 122.5449 1225.449
155-160 3 157.5 -17.07 291.3849 874.1547
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
Sum = 4748.8005
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93 358.3449 358.3449
185-190 11 187.5 12.93 167.1849 1839.0339
179-184 5 181.5 6.93 48.0249 240.1245
173-178 7 175.5 0.93 0.8649 6.0543
167-172 8 169.5 -5.07 25.7049 205.6392
161-166 10 163.5 -11.07 122.5449 1225.449
155-160 3 157.5 -17.07 291.3849 874.1547
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
s2 = 93.10744
8005.4748
Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution TableClass f
191-196 1 193.5 18.93 358.3449 358.3449
185-190 11 187.5 12.93 167.1849 1839.0339
179-184 5 181.5 6.93 48.0249 240.1245
173-178 7 175.5 0.93 0.8649 6.0543
167-172 8 169.5 -5.07 25.7049 205.6392
161-166 10 163.5 -11.07 122.5449 1225.449
155-160 3 157.5 -17.07 291.3849 874.1547
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mean=174.57
xxm mx 2xxm 2xxf m
s = 39.1093.107
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Sum = 1206
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Sum = 1206 MEAN= 8.2645
1206
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
MEDIAN CLASS
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Median= 8.26315
112
45
5.24
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
MODAL CLASS
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f Xm fXm LB UB <cf >cf
40 – 42 1 41 41 39.5 42.5 45 1
37 – 39 0 38 0 36.5 39.5 44 1
34 – 36 2 35 70 33.5 36.5 44 3
31 – 33 2 32 64 30.5 33.5 42 5
28 – 30 14 29 406 27.5 30.5 40 19
25 – 27 15 26 390 24.5 27.5 26 34
22 – 24 5 23 115 21.5 24.5 11 39
19 – 21 6 20 120 18.5 21.5 6 45
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
Mode= 23.273110
105.24
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2
37 – 39 0 38 11.2
34 – 36 2 35 8.2
31 – 33 2 32 5.2
28 – 30 14 29 2.2
25 – 27 15 26 -0.8
22 – 24 5 23 -3.8
19 – 21 6 20 -6.8
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2 201.64
37 – 39 0 38 11.2 125.44
34 – 36 2 35 8.2 67.24
31 – 33 2 32 5.2 27.04
28 – 30 14 29 2.2 4.84
25 – 27 15 26 -0.8 0.64
22 – 24 5 23 -3.8 14.44
19 – 21 6 20 -6.8 46.24
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2 201.64 201.64
37 – 39 0 38 11.2 125.44 0
34 – 36 2 35 8.2 67.24 134.48
31 – 33 2 32 5.2 27.04 54.08
28 – 30 14 29 2.2 4.84 67.76
25 – 27 15 26 -0.8 0.64 9.6
22 – 24 5 23 -3.8 14.44 72.2
19 – 21 6 20 -6.8 46.24 277.44
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2 201.64 201.64
37 – 39 0 38 11.2 125.44 0
34 – 36 2 35 8.2 67.24 134.48
31 – 33 2 32 5.2 27.04 54.08
28 – 30 14 29 2.2 4.84 67.76
25 – 27 15 26 -0.8 0.64 9.6
22 – 24 5 23 -3.8 14.44 72.2
19 – 21 6 20 -6.8 46.24 277.44
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2 201.64 201.64
37 – 39 0 38 11.2 125.44 0
34 – 36 2 35 8.2 67.24 134.48
31 – 33 2 32 5.2 27.04 54.08
28 – 30 14 29 2.2 4.84 67.76
25 – 27 15 26 -0.8 0.64 9.6
22 – 24 5 23 -3.8 14.44 72.2
19 – 21 6 20 -6.8 46.24 277.44
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
Sum = 817.2
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2 201.64 201.64
37 – 39 0 38 11.2 125.44 0
34 – 36 2 35 8.2 67.24 134.48
31 – 33 2 32 5.2 27.04 54.08
28 – 30 14 29 2.2 4.84 67.76
25 – 27 15 26 -0.8 0.64 9.6
22 – 24 5 23 -3.8 14.44 72.2
19 – 21 6 20 -6.8 46.24 277.44
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
s2 = 57.1844
2.817
Test Scores of 45 Students in Math 8
Grouped Frequency Distribution TableClass f
40 – 42 1 41 14.2 201.64 201.64
37 – 39 0 38 11.2 125.44 0
34 – 36 2 35 8.2 67.24 134.48
31 – 33 2 32 5.2 27.04 54.08
28 – 30 14 29 2.2 4.84 67.76
25 – 27 15 26 -0.8 0.64 9.6
22 – 24 5 23 -3.8 14.44 72.2
19 – 21 6 20 -6.8 46.24 277.44
Learning Objective: The students should be able to calculate the measures of variability of grouped data.
xxm mx 2xxm 2xxf m
Mean=26.8
s = 31.457.18
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