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Question

Find the mean, median and mode of the following data:
Class05050100100150150200200250250300300350Frequency2356531


Solution

Class05050100100150150200200250250300300350Frequency2356531cf251016212425

N = 25 N2=12.5

Median class = 150 - 200

Here, l = 150, f = 6, F = 10, h = 50

Median class = 150 - 200

Here, l = 150, f = 6, F = 10 , h = 50

Median = l +(N2Ff)×

= 150 + (12.5106× 50

= 150 + 20.83 =  170.83

Modal class = 150 -200

l = 150. f1 = 5 f2= 5 f = 6  h = 50

Mode = l + ff12ff1f2 × h

Mode = 150​​​​​​​+  651255 × 50

Mode = ​​​​​​​ 150​​​​​​​+ ​​​​​​​ 25 = 175

By empirical formula;

Mode = 3 median - 2 mean

175 = 3 × 170.83 - 2mean

mean = 168.74

Hence, mean = 168.74, median = 170.83, Mode = 175


Mathematics
Secondary School Mathematics X
Standard X

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