If the mean of the following frequency distribution is 24, find the value of p.


Class



0 - 10



10 - 20



20 - 30



30 - 40



40 - 50



Frequency



3



4



p



3



2


For equal class intervals, we will solve by finding mid points of these classes using direct method.


CLASS



MID - POINT(xi)



FREQUENCY(fi)



fixi



0 - 10



5



3



15



10 - 20



15



4



60



20 - 30



25



p



25p



30 - 40



35



3



105



40 - 50



45



2



90



TOTAL




12 + p



270 + 25p



We have got


Σfi = 12 + p & Σfixi = 270 + 25p


∵ mean is given by



⇒


⇒ 288 + 24p = 270 + 25p


⇒ 25p – 24p = 288 – 270


⇒ p = 18


Thus, p is 18


8