Question

find the value of the missing variate for the following distribution whose mean is 10 variate (xi) 5, 7, 9, 11,---,15, 20 frequency(fi) 4, 4, 4, 7, 3, 2, 1

Answer 1

here is your answer

Answer 2

The missing variate for the given distribution x is 13

Step-by-step explanation:

Given data for the following distribution is

Variate $x_i$       5, 7, 9, 11,---,15, 20

Frequency$f_i$  4, 4, 4, 7, 3, 2, 1

And also given that mean=10

To find the missing variate :

Let x be the missing variate

$x_i$      $f_i$       $x_if_i$

5       4          20

7       4           28

9      4           36

11      7          77

x       3           3x

15     2         30

20     1        20

________________________

   $\sum f_i=25$   $\sum x_if_i=211+3x$

______________________

We know that $Mean=\frac{\sum x_if_i}{\sum\f_i}$

• $10=\frac{211+3x}{25}$
• $10\times 25=211+3x$
• $250=211+3x$
• $250-211=3x$
• $39=3x$
• Rewritting the equation
• $3x=39$
• $x=\frac{39}{3}$
• $=13$
• Therefore x=13

Therefore the missing variate x is 13