Q4 of 55 Page 340

If the arithmetic mean of the distribution given below is 15, let us find the value of p.

We have been given the arithmetic mean of the data, that is, 15.

⇒ Mean = 15


To find the value of p, we need to simply find mean using direct method.


So, let’s make a table showing frequencies and fixi.



So, we get


∑fixi = 445 + 10p


∑fi = 27 + p


Using direct method, we have the formula of arithmetic mean as follows:



⇒ [∵ Mean = 15, ∑fixi = 445 + 10p & ∑fi = 27 + p]


⇒ 15 (27 + p) = 445 + 10p


⇒ 405 + 15p = 445 + 10p


⇒ 15p – 10p = 445 – 405


⇒ 5p = 40


⇒


⇒ p = 8


Thus, p = 8.

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