If the arithmetic

We have been given the arithmetic mean of the data, that is, 20.6.

⇒ Mean = 20.6

To find the value of a, 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 = 530 + 25a

∑f_i = 50

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

⇒ [∵ Mean = 20.6, ∑f_ix_i = 530 + 25a & ∑f_i = 50]

⇒ 1030 = 530 + 25a

⇒ 25a = 1030 – 530

⇒ 25a = 500

⇒

⇒ a = 20

Thus, a = 20.