Q) Literacy rates of 40 cities are given in the following table. It is given that mean literacy rate is 63.5, then find the
missing frequencies x and y.

Ans:

Step 1: Let’s re-organize the data in the frequency table to find out each part:

Step 2: Given that the total of frequencies = 40

∴  31 + x + y = 40

∴  x + y = 40 – 31

∴  x + y = 9 ……… (i)

Step 3: We know that, mean of grouped data =

∴ 63.5 =

∴ 63.5 =

∴ 63.5 x 40 = 2057.5 + 52.5 x + 57.5 y

∴ 2540 = 2057.5 + 52.5 x + 57.5 y

∴ 2540 – 2057.5 = 2.5 (21 x + 23 y)

∴ 482.5 = 2.5 (21 x + 23 y)

∴ 21 x + 23 y =

∴  21 x + 23 y = 193 ………. (ii)

Step 4: By multiplying equation (i) by 21 and subtract from equation (ii), we get:

(21 x + 23 y) – 21 (x + y) = 193 – 21 (9)

∴ 21 x + 23 y – 21 x – 21 y = 193 – 189

∴ 2 y = 4

 ∴ y =

 ∴ y = 2

Step 5: By substituting value of y in equation (i), we get:

x + y = 9

∴ x + 2 = 9

∴ x = 9 – 2

∴ x = 7

Therefore, the values of missing frequencies, x and y are 7 and 2 respectively.

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