measures of central tendency and variability for grouped data
TRANSCRIPT
![Page 1: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/1.jpg)
GROUPED DATAMeasures of Variability
![Page 2: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/2.jpg)
LEARNING OBJECTIVE
At the end of the period, the students
should be able to calculate the
measures of variability of grouped
data.
![Page 3: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/3.jpg)
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.
![Page 4: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/4.jpg)
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.
![Page 5: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/5.jpg)
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.
![Page 6: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/6.jpg)
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.
![Page 7: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/7.jpg)
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
![Page 8: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/8.jpg)
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
![Page 9: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/9.jpg)
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
![Page 10: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/10.jpg)
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
![Page 11: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/11.jpg)
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
![Page 12: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/12.jpg)
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
![Page 13: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/13.jpg)
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
![Page 14: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/14.jpg)
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
![Page 15: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/15.jpg)
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.
![Page 16: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/16.jpg)
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
![Page 17: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/17.jpg)
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
![Page 18: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/18.jpg)
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.
![Page 19: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/19.jpg)
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.
![Page 20: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/20.jpg)
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
![Page 21: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/21.jpg)
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.
![Page 22: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/22.jpg)
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.
![Page 23: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/23.jpg)
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.
![Page 24: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/24.jpg)
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
![Page 25: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/25.jpg)
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
![Page 26: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/26.jpg)
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.
![Page 27: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/27.jpg)
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.
![Page 28: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/28.jpg)
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
![Page 29: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/29.jpg)
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
![Page 30: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/30.jpg)
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
![Page 31: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/31.jpg)
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
![Page 32: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/32.jpg)
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
![Page 33: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/33.jpg)
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
![Page 34: Measures of Central Tendency and Variability for Grouped Data](https://reader034.vdocuments.site/reader034/viewer/2022052405/58f0b5721a28abd8278b458b/html5/thumbnails/34.jpg)
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
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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