# 13. Find the mean, mode and median for the following data:Classes 0-10 10-20 20-30 30-40 40-50 50-60 60-70Frequency 5 8 15 20 14 8 5

according to given observation:

 class interval (CI) frequency f cumulative frequency midpoint of CI (x) fx 0-10 5 5 5 25 10-20 8 13 15 120 20-30 15 28 25 375 30-40 20 48 35 700 40-50 14 62 45 630 50-60 8 70 55 440 60-70 5 75 65 325 75 2615

mean =

to find the median : we will apply the formula ;

median =

75/ 2 = 37.5.

this lies in the interval 30-40.

i = size of the class interval

L = lower limit of the CI which includes the median score.

F = cumulative frequency up to median CI

f = frequency in the class interval that contains the median.

therefore L = 30 ; F = 28 ; f = 20 ; i =10

thus median =

mode =

where

L = lower class boundary of modal class

the frequency of the modal class

previous frequency of the modal class

the next frequency of the modal class

i = size of the modal class

modal class is the class with maximum frequency

from the observation: maximum frequency = 20.

modal class = 30-40

L = 30 ; 20 ; 15 and 14 ; i = 10

mode =

= 30 + (5/11)

= 30 + 0.4545

= 30.4545

hope this helps you.

cheers!!

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