Question

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Answer 1

$\textbf{Solution:}$

$\text{Let n_1 and n_2 be the number of boys and girls respectively}$

$\text{Let x_1 and x_2 be the mean heights of boys and girls respectly}$

$\text{Let \overline{x} be the combined mean height of boys and girls}$

$\text{Here,}$

$n_1=14$

$\text{Total number of students =32}$

$\implies\,n_1+n_2=32$

$\implies\,n_2=18$

$\overline{x_1}=1.56$

$\text{By using the combined mean formula}$

$\bf\overline{x}=\dfrac{n_1\;\overline{x_1}+n_2\;\overline{x_2}}{n_1+n_2}$

$1.515=\dfrac{14(1.56)+18\;\overline{x_2}}{32}$

$48.48=21.84+18\;\overline{x_2}$

$48.48-21.84=18\;\overline{x_2}$

$26.64=18\,\overline{x_2}$

$\overline{x_2}=\dfrac{26.64}{18}$

$\implies\bf\overline{x_2}=1.48\,\text{m}$

$\therefore\textbf{The mean height of the girls is 1.48 m}$

Find more:

The average mark of a class is 35. There are 5 girls and their average is 15. The remaining boys have 39 as their average mark. The no of students in the class is

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Answer 2

Answer:

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Step-by-step explanation:

Given as :

Total number of students in class = 32

number of boys + number of girls = 32

The mean height of 32 students = 1.515

The mean height of 14 boys = 1.56

The mean height of girls = x

Let The number of boys = b

Let The number of girls = g

According to question

∵The mean height of students = 1.515

Total number of students = 32

So, Total height of 32 students = 32 × 1.515

i.e Total height of 32 students = 48.48

Again

As number of girls = g

So, g  = 32 - 14

i.e g = 18

∴ 14 × 1.56 + 18 × x  = 48.48

Or, 21.84 + 18 x = 48.48

Or, 18 x = 26.64

∴   x =

i.e  x = 1.48

So, The mean of girls student = x = 1.48

Hence, The mean of 18 girls students is 1.48  Answer

The mean of 18 girls students is 1.48