Q3 of 40 Page 210

If the mean of the following frequency distribution is 7.2 find value of ‘K’.





















X



2



4



6



8



10



12



F



4



7



10



16



K



3



Given is the frequency distribution table for ungrouped data.

We have












































X


(xi)



F


(frequency)


(fi)



xifi



2



4



2 × 4 = 8



4



7



4 × 7 = 28



6



10



6 × 10 = 60



8



16



8 × 16 = 128



10



K



10 × K = 10K



12



3



12 × 3 = 36



TOTAL



∑fi = 40 + K



∑xifi = 260 + 10K



Mean of such ungrouped data is given by



⇒


⇒ [∵, Mean = 7.2]


⇒ 7.2(40 + K) = 260 + 10K


⇒ 288 + 7.2K = 260 + 10K


⇒ 10K – 7.2K = 288 – 260


⇒ 2.8K = 28


⇒ K = 28/2.8


⇒ K = 10


Thus, K = 10.


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