If the arithmetic

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 f_ix_i.

So, we get

∑f_ix_i = 445 + 10p

∑f_i = 27 + p

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

⇒ [∵ Mean = 15, ∑f_ix_i = 445 + 10p & ∑f_i = 27 + p]

⇒ 15 (27 + p) = 445 + 10p

⇒ 405 + 15p = 445 + 10p

⇒ 15p – 10p = 445 – 405

⇒ 5p = 40

⇒

⇒ p = 8

Thus, p = 8.