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# Ex.14.1 Q9 Statistics Solution - NCERT Maths Class 10

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## Question

The following table gives the literacy rate (in percentage) of $$35$$ cities. Find the mean literacy rate.

 Literacy rate (in %) $$45 – 55$$ $$55 – 65$$ $$65 – 75$$ $$75 – 85$$ $$85 – 95$$ Number of cities $$3$$ $$10$$ $$11$$ $$8$$ $$3$$

Video Solution
Statistics
Ex 14.1 | Question 9

## Text Solution

What is known?

The Literacy rate (in percentage) of $$35$$ cities

What is unknown?

The Mean literacy rate.

Reasoning:

We solve this question by assumed mean method.

Mean, $$\overline x = a + \left( {\frac{{\sum {{f_i}{d_i}} }}{{\sum {{f_i}} }}} \right)$$

Steps:

We know that,

Class mark, $${x_i} = \frac{{{\text{Upper class limit }} + {\text{ Lower class limit}}}}{2}$$

Taking assumed mean$$, a=70$$

 Literacy rate No of cities$$(f_i)$$ $$X_i$$ $$d_i = x_i -a$$ $$f_id_i$$ $$45 – 55$$ $$3$$ $$50$$ $$-20$$ $$-60$$ $$55 – 65$$ $$10$$ $$60$$ $$-10$$ $$-100$$ $$65 – 75$$ $$11$$ $$70(a)$$ $$0$$ $$0$$ $$75 – 85$$ $$8$$ $$80$$ $$10$$ $$80$$ $$85 – 95$$ $$3$$ $$90$$ $$20$$ $$60$$ $$\Sigma f_i=35$$ $$\Sigma f_id_i=-20$$

From the table,we obtain

$\begin{array}{l}\sum {{f_i} = 35} \\\sum {{f_i}{d_i}} = - 20\end{array}$

\begin{align} \text { Mean }(\overline{{x}}) &={a}+\left(\frac{\Sigma f_{i} d_{i}}{\Sigma {f}_{{i}}}\right) \\ \overline{{x}} &=70+\left(\frac{-20}{35}\right) \\ \overline{{x}} &=70-\frac{4}{7} \\ \overline{{x}} &=70-0.57 \\ \overline{{x}} &=69.43 \end{align}

Thus, the mean literacy rate is $$69.43$$%

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