If the arithmetic mean of the following distribution is 1.46. Find the missing frequencies.

We know that,

Where, = Mean, x_i = values of x and f_i = frequency for that x.

Let first missing frequency be ‘y’ and second one be ‘z’.

⇒ 292 - 140 = y + 2z

⇒ y + 2z = 152……… (1)

Also, 46 + y + z + 25 + 10 + 5 = 200

⇒ y + z = 200 - 86

⇒ y + z = 114

⇒ y = 114 - z

Substituting this in (1), we get -

⇒ 114 - z + 2z = 152

⇒ z = 38

∴, y = 114 - 38

⇒ 76

⇒ The missing frequencies are - 76 and 38.