Question

calculate arithmetic mean from the following frequency distribution
X. f
0-10. 3
10-20. 9
20-30. 15
30-40. 30
40-50. 18
50-60. 5

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Answer 1

Explanation:

as of mean, formula is to add the add the data and then divide it with the sum of the data, ∑ , this sign means sum and here X is the data, f means frequency which means the number of the data.

According to the formula,

sum of data / no of data

it comes, ∑Xf / N

here the data are in continuous form, so we cant have an exact number of the data, so we take the mid value from the data, eg. for 0-10 the mid value would be ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) 5. this mid value would be named as 'm'.

atlast, we get the formula to calculate this data ∑fm/N. As we couldnt get exact data for X.

now calculation,

Solution,

calculate the values of ∑fm and N,

X                     f             m                 fm

0-10.               3              5                 (3x5= 15)15

10-20.             9              15                  135

20-30             15            25                  375

30-40.            30           35                   1050

40-50.            18            45                   810

50-60             5             55                  275

                 N=80                          ∑fm= 2660

now,

Mean=∑fm / N

        = 2660 / 80

        = 33.25

the mean is 33.25.

Took a long time to answer, hope my explanation helps!