Mean of the Tabulated Data

In the mean of the tabulated data, if the frequencies of n observations

x1, x2, x3, ………. xn are f1, f2, f3 ………. fn, then

Mean of the tabulated data
= (f1x1 + f2x2 + f3x3 ……… fnxn)/( f1 + f2 + f3 ………. fn) = (∑ fixi)/(∑fi)

Worked-out examples on mean of the tabulated data:

1. Find the mean weight of 50 girls from the following table.

Weight in kg 40 42 34 36 46
No. of girls 6 6 15 14 7


Solution:

Mean = (f1x1 + f2x2 + f3x3 + f4x4 + f5x5)/(f1 + f2 + f3 + f4 + f5)

     = (40 × 6 + 42 × 6 + 34 × 15 + 36 × 14 + 46 × 7)/(8 + 6 + 15 + 14 + 7)

     = (240 + 252 + 510 + 504 + 322)/50

     = 1828/50

     = 36.56




2. If the mean of the following frequency distributions is 9, find the value of `a’. Write the tally marks also.

Variable (xi) 4 6 8 10 12 15
Frequency (fi) 8 9 17 a 8 4


Solution:

Frequency distribution table

Frequency Distribution Table
Mean = (∑fixi)/(∑fi)

But given mean = 9

So, we have (378 + 10a)/(46 + a) = 9

378 + 10a = 9(46 + a)

378 + 10a = 414 + 9a

10a - 9a = 414 - 378

a = 36

Statistics



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