Question

2 Find the average of 12 numbers if the average of the first nine numbers is
21 and the average of the last three is 17.​

Answer 1

Answer:

average of first nine number is 21

sum of first nine number is 21×9=189

average of last three number is 17

sum of last three numbers is 17×3=51

so sum of 12 numbers is (189+51)=240

average of 12 number is 240/12=20

Answer 2

Given Question:-

• Find the average of 12 numbers if the average of the first nine numbers is 21 and the average of the last three is 17.

Answer

According to statement, the data is divided in to 2 groups.

Group 1

$\sf \: Number \: of \: observations, \: n_1 = 9$

$\sf \: Mean \: of \: observations, \: \overline{x_1} = 21$

Group 2

$\sf \: Number \: of \: observations, \: n_2 = 3$

$\sf \: Mean \: of \: observations, \: \overline{x_2} = 17$

$\bf \: Let \: mean \: of \: 12 \: observations \: be \: {x_c}$

Now,

We know that

$:  \implies \bf \: {x_c} = \dfrac{{{n_1}{{\overline x }_1} + {n_2}{{\overline x }_2}}}{{{n_1} + {n_2}}}$

$:  \implies \tt \: {x_c} = \dfrac{21 \times 9 + 3 \times 17}{9 + 3}$

$:  \implies \tt \: {x_c} = \dfrac{189 + 51}{12}$

$:  \implies \tt \: {x_c} = \dfrac{240}{12}$

$:  \implies \boxed{ \red{ \bf \: {x_c} = 20}}$

$\large \boxed{ \pink{ \bf \: Hence \: mean \: of \: 12 \: observations \: be \: 20}}$