Compute the mean, median, mode and standard deviation for the following discrete probability distribution: `[[X:, 20, 30, 40, 50, 60],[F:,8, 12, 10, 12, 8]]`.

Expert Answers

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The value of the variable X and the frequency F are given as follows:

`[[X:, 20, 30, 40, 50, 60],[F:,8, 12, 10, 12, 8]]`

The mean is given by: `(sum(f*x))/(sum(f))`

=> `(20*8 + 30*12+10*40+50*12+60*8)/50`

=> `2000/50`

=> 40

The median is estimated from the cumulative frequency.

`[[X,20, 30, 40, 50, 60],[F,8, 12, 10, 12, 8],[CF,160,520,920,1520,2000]]`

The median is 40

The mode is 30 and 50

The standard deviation is `sqrt(400*8/50+100*12/50+0+100*12/50+400*8/50)`

= `sqrt 176`

= 13.26

Approved by eNotes Editorial Team
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