This is a presentation which covers the measures of central tendency and variability for grouped data.

1. GROUPED DATA
Measures of Variability

2. LEARNING OBJECTIVE
At the end of the period, the students
should be able to calculate the
measures of variability of grouped
data.

3. 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.

4. 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.

5. 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.

6. 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.

7. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 

8. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 

9. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 

10. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 

11. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 

12. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Sum =
4748.8005

13. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
s2 = 93.107
44
8005.4748


14. Height of 45 Students from Grade 8 in cm
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
s = 39.1093.107 

15. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

16. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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

17. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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= 8.26
45
1206


18. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

19. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

20. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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

21. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

22. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

23. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

24. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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= 8.263
15
11
2
45
5.24 
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













25. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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

26. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

27. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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.

28. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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= 23.273
110
10
5.24 








29. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean
=26.8

30. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean=
26.8

31. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean=
26.8

32. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean=
26.8

33. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean=
26.8
Sum =
817.2

34. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean=
26.8
s2 = 57.18
44
2.817


35. Test Scores of 45 Students in Math 8
Grouped Frequency Distribution Table
Class 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  2
xxm   2
xxf m 
Mean=
26.8
s = 31.457.18 