Math Assignment Help With Variance Of Grouped Data

10.3.3 Variance of grouped data:

Step Deviation Method: When data are grouped into a frequency distribution having class intervals of equal size h, the formula used is;

$variance of grouped data$

Example: Calculate the mean and standard deviation for the following distribution:

Marks	Number of students
20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90	3 6 13 15 14 5 4

Marks

Number of students

20 – 30

30 – 40

40 – 50

50 – 60

60 – 70

70 – 80

80 – 90

Solution: firstly let’s find the mid values of the class intervals and consider a suitable assumed mean, A

Class interval	Frequency fi	Mid-value xi	ui = xi – A/10	fi ui	fiui²
20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90	3 6 13 15 14 5 4	25 35 45 55 65 75 85	-3 -2 -1 0 1 2 3	-9 -12 -13 0 14 10 12	27 24 13 0 14 20 36
Σ fi = 60	Σfi ui = 2	Σfiui² = 134

Class interval

Frequency

Mid-value

ui = xi – A/10

fi ui

fiui²

20 – 30

30 – 40

40 – 50

50 – 60

60 – 70

70 – 80

80 – 90

-3

-2

-1

-9

-12

-13

Σ fi = 60

Σfi ui = 2

Σfiui² = 134

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