Question

if mean of 4 numbers is 27 and that of next 5 numbers is 18. Find the mean of all the numbers

Answer 1

Answer:

The mean of all the number is 22.

Step-by-step-explanation:

Let the total 9 numbers be N₁, N₂, N₃,.... N₇, N₈, N₉.

We have given that,

Mean of first 4 numbers is 27.

$\displaystyle{\sf\:\therefore\:Mean\:=\:\dfrac{N_1\:+\:N_2\:+\:N_3\:+\:N_4}{4}}$

$\displaystyle{\implies\sf\:\dfrac{N_1\:+\:N_2\:+\:N_3\:+\:N_4}{4}\:=\:27}$

$\displaystyle{\implies\sf\:N_1\:+\:N_2\:+\:N_3\:+\:N_4\:=\:27\:\times\:4}$

$\displaystyle{\implies\sf\:N_1\:+\:N_2\:+\:N_3\:+\:N_4\:=\:108}$

We have given that,

Mean of next 5 numbers is 18.

$\displaystyle{\sf\:\therefore\:Mean\:=\:\dfrac{N_5\:+\:N_6\:+\:N_7\:+\:N_8\:+\:N_9}{5}}$

$\displaystyle{\implies\sf\:\dfrac{N_5\:+\:N_6\:+\:N_7\:+\:N_8\:+\:N_9}{5}\:=\:18}$

$\displaystyle{\implies\sf\:N_5\:+\:N_6\:+\:N_7\:+\:N_8\:+\:N_9\:=\:18\:\times\:5}$

$\displaystyle{\implies\sf\:N_5\:+\:N_6\:+\:N_7\:+\:N_8\:+\:N_9\:=\:90}$

Now, mean of all the numbers is given by,

$\displaystyle{\pink{\sf\:Mean\:=\:\dfrac{Sum\:of\:all\:numbers}{9}}}$

$\displaystyle{\implies\sf\:Mean\:=\:\dfrac{N_1\:+\:N_2\:+\:N_3\:+\:N_4\:+\:N_5\:+\:N_6\:+\:N_7\:+\:N_8\:+\:N_9}{9}}$

$\displaystyle{\implies\sf\:Mean\:=\:\dfrac{108\:+\:90}{9}}$

$\displaystyle{\implies\sf\:Mean\:=\:\cancel{\dfrac{198}{9}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:Mean\:=\:22\:}}}}$

∴ The mean of all the number is 22.

Answer 2

Question :-

• If mean of 4 numbers is 27 and that of next 5 numbers is 18. Find the mean of all the numbers

Required Answer :-

➧ Given That :-

• ➻ The mean of 4 numbers is 27

• ➻ The mean of next 5 numbers is 18

➧ To Find

➻ The mean of all numbers

➧ Formula :-

➽ Sum of all Observation

➻ Mean × Number of observation

➧ Explanation :-

➽ Sum of 4 numbers

• ➻ = 4 × 27 = 108

➽ Sum of 5 numbers

• ➻ = 5 × 18 = 90

➽ Sum of all 9 numbers

• ➻ 108 + 90
• ➻ 198

➧ Formula :-

• ➻ Formula to calculate mean

• ➻ Mean = sum of observation / Total number of observation

➧ Required Mean

• ➻ 198 ÷ 9 = 22

➧ Therefore :-

• ➻ The mean of all observation is 22.

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