# Ex.14.3 Q7 Statistics Solution - NCERT Maths Class 10

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## Question

The distribution below gives the weights of $$30$$ students of a class. Find the median weight of the students.

 Weight (in kg) $$40-45$$ $$45-50$$ $$50-55$$ $$55-60$$ $$60-65$$ $$65-70$$ $$70-75$$ Number of students $$2$$ $$3$$ $$8$$ $$6$$ $$6$$ $$3$$ $$2$$

## Text Solution

What is known?

The weights of $$30$$ students of a class.

What is unknown?

The median weight of the students.

Reasoning:

Median Class is the class having Cumulative frequency $$(cf)$$ just greater than $$\frac n{2}$$

Median $$= l + \left( {\frac{{\frac{n}{2} - cf}}{f}} \right) \times h$$

Class size,$$h$$

Number of observations,$$n$$

Lower limit of median class,$$l$$

Frequency of median class,$$f$$

Cumulative frequency of class preceding median class,$$cf$$

Steps:

 Weight (in kg) Number of students $$f$$ Cumulative frequency $$cf$$ $$40-45$$ $$2$$ $$2$$ $$45-50$$ $$3$$ $$2 + 3 = 5$$ $$50-55$$ $$8$$ $$5 + 8 = 13$$ $$55-60$$ $$6$$ $$13 + 6 = 19$$ $$60-65$$ $$6$$ $$19 + 6 = 25$$ $$65-70$$ $$3$$ $$25 + 3 = 2$$ $$70-75$$ $$2$$ $$28 + 2 = 30$$ $$n=30$$

From the table, it can be observed that

$$n = 30{\rm{ }} \Rightarrow \frac{n}{2} = 15$$

Cumulative frequency $$(cf)$$ just greater than $$15$$ is $$19,$$ belonging to class $$55 – 60.$$

Therefore, median class $$=55 – 60$$

Class size$$, h = 5$$

Lower limit of median class$$, l = 55$$

Frequency of median class$$, f = 6$$

Cumulative frequency of class preceding median class, $$cf = 13$$

Median $$= l + \left( {\frac{{\frac{n}{2} - cf}}{f}} \right) \times h$$

$\begin{array}{l} = 55 + \left( {\frac{{15 - 13}}{6}} \right) \times 5\\ = 55 + \frac{2}{6} \times 5\\ = 55 + \frac{5}{3}\\ = 55 + 1.67\\ = 56.67 \end{array}$

Therefore, median weight is $$56.67 \rm\,kg.$$

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