Question

If the mean of the following data is 59, find the missing frequency.

Class 10-30 30-50 50-70 70-90 90-110

Frequency 10 7 5 X 12​

Answer 1

Step-by-step explanation:

Given:Mean of the following data is 59.

$\begin{array}{|c|c|}</p><p>\cline{1-2} Class& Frequency\\</p><p>\cline{1-2} 10-30& 10\\</p><p>\cline{1-2} 30-50& 7\\</p><p>\cline{1-2} 50-70& 5\\</p><p>\cline{1-2} 70-90& X\\</p><p>\cline{1-2} 90-110& 12\\\cline{1-2}</p><p>\end{array}$

To find: X

Solution:

We know that

$Mean = \frac{ \Sigma \: x_if_i}{ \Sigma \: f_i}$

Find class mark for each class and put the values in the formula,in order to find X

$\begin{array}{|c|c|c|c|}</p><p>\cline{1-4} Class& Frequency& x_i&x_if_i\\</p><p>\cline{1-4} 10-30& 10&20&200\\</p><p>\cline{1-4} 30-50& 7& 40&280\\</p><p>\cline{1-4} 50-70& 5& 60&300\\</p><p>\cline{1-4} 70-90& X& 80&80X\\</p><p>\cline{1-4} 90-110& 12& 100&1200\\</p><p>\cline{1-4}Total&34+X&&1980+80X\\\cline{1-4}</p><p>\end{array}$

Put the values

$59 = \frac{1980 + 80X}{34 + X} \\ \\ cross \: multiply \\ \\ 59(34 + X) = 1980 + 80X\\ \\ 59 \times 34 + 59X = 1980 + 80X \\ \\ 59X - 80X = 1980 -2006 \\ \\ - 21X = -26 \\ \\ 21X =26 \\ \\ X =1.24$

Thus,

Value of missing frequency is 1.24

Which is not possible.

Frequency should be positive integer.

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Hope it helps you.

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Answer 2

Answer:

X=1.24 is your answer.....