Question

The mean of following distribution is 25. If total frequency is 106 find the missing frequencies.
x 19 21 23 25 27 29 31
f 13 15 f1 18 16 f2 13

Answer 1

Step-by-step explanation:

hope this answer will be helpful

Answer 2

The missing frequencies are $f_1=16$ and $f_2=15$

Step-by-step explanation:

Given that the mean of the following data is 25 and total frequency is 106

It can be written as $\sum f=106$

The given data is

x         f           fx

19       13                      247

21       15                       315

23      $f_1$                         $23f_1$

25      18                       450

27       16                       432

29      $21f_1$                      $29f_2$

31         13                       403

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      $\sum f=75+f_1+f_2$    $\sum fx=1847+23f_1+29f_2$

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$\sum f=75+f_1+f_2=106$ ( since $\sum f=106$ )

$75+f_1+f_2=106$

$f_1+f_2=106-75$

$f_1+f_2=31\hfill (1)$

Equation (1) implies that $f_1=31-f_2$

$\sum fx=1847+23f_1+29f_2$  

$Mean=\frac{\sum fx}{\sum f}$

$25=\frac{1847+23f_1+29f_2}{75+f_1+f_2}$ ( since mean=25 given )

$25(75+f_1+f_2)=1847+23(f_1)+29f_2$

$1875+25f_1+25f_2-1847-23f_1-29f_2=0$

$28+2f_1-4f_2=0$

$28+2(31-f_2)-4f_2=0$

$28+2(31)-2f_2-4f_2=0$

$28+62-2f_2-4f_2=0$

$-6f_2=-90$

$f_2=\frac{90}{6}$

$f_2=15$

Substitute the value of $f_2=15$ in equation (1) we get

$f_1+15=31$

$f_1=31-15$

$f_1=16$

Therefore the missing frequencies are $f_1=16$ and $f_2=15$