3 Mark Question

Question 13 Marks

Following $10$ observations are arranged in ascending order as follows. $2, 3 , 5 , 9, x + 1, x + 3, 14, 16, 19, 20.$ If the median of the data is $11,$ find the value of $x.$

Answer

Given data in ascending order :
$2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20.$
$\therefore$ Number if observations $(n) = 10$ (i.e., even)
$\therefore$ Median is the average of middle two observations
Here, the 5th and 6th numbers are in the middle position.
$\therefore \text { Median }=\frac{(x+1)+(x+3)}{2}$
$\therefore 11=\frac{2 x+4}{2}$
$\therefore 22=2 x+4$
$\therefore 22-4=2 x$
$\therefore 18=2 x$
$\therefore x=9$

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Question 23 Marks

The monthly salaries in rupees of 30 workers in a factory are given below.
5000, 7000, 3000, 4000, 4000, 3000, 3000,
3000, 8000, 4000, 4000, 9000, 3000, 5000,
5000, 4000, 4000, 3000, 5000, 5000, 6000,
8000, 3000, 3000, 6000, 7000, 7000, 6000,
6000, 4000
From the above data find the mean of monthly salary.

Answer

$\begin{aligned} \operatorname{Mean}(\bar{x}) & =\frac{\sum f_i x_i}{\sum f_i} \\ & =\frac{1,47,000}{30} \\ & =₹ 4900\end{aligned}$
∴ The mean of monthly salary is ₹ 4900.

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Question 33 Marks

The first unit test of 40 marks was conducted for a class of 35 students. The marks obtained by the students were as follows. Find the mean of the marks.
40, 35, 30, 25, 23, 20, 14, 15, 16, 20, 17, 37, 37, 20, 36, 16, 30, 25, 25, 36, 37, 39, 39, 40, 15, 16, 17, 30, 16, 39, 40, 35, 37, 23, 16.

Answer

Here, we can add all observations, but it will be a tedious job. It is easy to make frequency distribution table to calculate mean.

$\begin{aligned} \operatorname{Mean}(\bar{x}) & =\frac{\sum f_i x_i}{ N } \\ & =\frac{956}{35}\end{aligned}$
= 27.31 marks (approximately)
∴ The mean of the mark is 27.31.

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Question 43 Marks

A sports club has organised a table-tennis tournaments. The following table gives the distribution of players ages. Find the cumulative frequencies equal to or more than the lower class limit and complete the table

Answer

Equal to lower limit or more than lower limit type of cumulative table.

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Question 53 Marks

38 people donated to an organisation working for differently abled persons. The amount in rupees were as follows:
101, 500, 401, 201, 301, 160, 210, 125, 175,
190, 450, 151, 101, 351, 251, 451, 151, 260,
360, 410, 150, 125, 161, 195, 351, 170, 225,
260, 290, 310, 360, 425, 420, 100, 105, 170, 250, 100
i. By taking classes 100 – 149, 150 – 199, 200 – 249… prepare grouped frequency distribution table.
ii. From the table, find the number of people who donated ₹350 or more.

Answer

ii. Number of people who donated ₹ 350 or more = 4 + 4 + 2 + 1 = 11

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Question 63 Marks

In a village, the milk was collected from 50 milkmen at a collection center in litres as given below:
27, 75, 5, 99, 70, 12, 15, 20, 30, 35, 45, 80, 77,
90, 92, 72, 4, 33, 22, 15, 20, 28, 29, 14, 16, 20,
72, 81, 85, 10, 16, 9, 25, 23, 26, 46, 55, 56, 66,
67, 51, 57, 44, 43, 6, 65, 42, 36, 7, 35
By taking suitable classes, prepare grouped frequency distribution table.

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Question 73 Marks

In a school, 46 students of 9th standard, were told to measure the lengths of the pencils in their compass-boxes in Centimetres. The data collected was as follows:
16, 15, 7, 4.5, 8.5, 5.5, 5, 6.5, 6, 10, 12, 13,
4.5, 4.9, 16, 11, 9.2, 7.3, 11.4, 12.7, 13.9, 16,
5.5, 9.9, 8.4, 11.4, 13.1, 15, 4.8, 10, 7.5, 8.5,
6.5, 7.2, 4.5, 5.7, 16, 5.7, 6.9, 8.9, 9.2, 10.2, 12.3, 13.7, 14.5, 10
By taking exclusive classes 0-5, 5-10, 10-15,…. prepare a grouped frequency distribution table.

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Maths 3 Mark Question

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