Assertion Reason Maths Chapter 14: Statistics CBSE 10th

Assertion Reason Mathematics Chapter 14: Statistics CBSE 10th for Class 10th is very important as assertion reason and Case Study Based Passages have been introduced by CBSE in 2020. Assertion reason and Case Study Type of questions helps students to think Critically on every aspects of life.

Here is a collection of few questions for CBSE Class 10th Term 2 Exams. These Assertion Reason Questions are fully solved. 

Directions: Mark the option which is most suitable :
(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If both assertion and reason are false.

Question.1.
Assertion : Consider the following frequency distribution:

Class Interval3-66-99-1212-1515-1818-21
Frequency2521231012

The mode of the above data is 12.4.
Reason : The value of the variable which occurs most often is the mode.

(b) : Clearly, Reason is correct.
The maximum frequency is 23 and the modal class is 12–15.
So, `l` = 12, `f_{i}` = 23, `f_{0}` = 21, `f_{2}` = 10 and `h` = 3
`\therefore` Mode = `12+\left(\frac{23-21}{2\times 23-21-10}\right) \times 3`
= `\left(12+3\times \frac{2}{15}\right)`
= 12.4
`\therefore` Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

Question.2.
Assertion : If the value of mode and mean is 60 and 66 respectively, then the value of median is 64.
Reason : Median = (mode + 2 mean)

(c) Assertion is true but reason is false.
Median =`\frac{1}{3}`(mode + 2 mean)
= `\frac{1}{3}(60+2\times 66)`
= 64

Question.3.
Assertion : The arithmetic mean of the following given frequency distribution table is 13.81.

x4710131619
f71015202530

Reason : `\overline{x}=\frac{\sum f_{i}x_{i}}{\sum f_{i}}`

(a) Both assertion and reason are true and reason is the correct explanation of assertion.
Both assertion and reason are true, reason is the correct explanation of the assertion.

Question.4.
Assertion : If the number of runs scored by 11 players of a cricket team of India are 5, 19, 42, 11, 50, 30, 21, 0, 52, 36, 27 then median is 30.
Reason : Median `=(\frac{n+1}{2})^{th}` value, if n is odd.

(d) Assertion is false but reason is true.
Arranging the terms in ascending order,
0, 5, 11, 19, 21, 27, 30, 36, 42, 50, 52
Median value `=(\frac{11+1}{2})^{th}`
= `6^{th}` value
= 27

Question.5.
Assertion : If the arithmetic mean of 5, 7, `x`, 10, 15 is `x`, then `x` = 9.25.
Reason : If `x_{1}`, `x_{2}`, `x_{3}`, …, `x_{n}` are `n` values of a variable `X`, then the arithmetic mean of these values is given by
`\frac{x_{1}+x_{2}+x_{3}+…+x_{n}}{2n}`.

(c) : If `x_{1}`, x_{2}, `x_{3}`, …, `x_{n}` are `n` values of a variable `X`, then the arithmetic mean of these values is given by
`\frac{x_{1}+x_{2}+x_{3}+…+x_{n}}{n}`
`\therefore` Reason is wrong.
Now, mean of given values = `x` [Given]
⇒ `\frac{5+7+x+10+15}{5}` = `x`
⇒ `\frac{37+x}{5}` = `x`
⇒ `37 + x` = `5x`
⇒ `37` = `4x`
⇒ `x` = `9.25`, which is correct
`\therefore` Assertion is correct but Reason is wrong.

Question.6.
Assertion : Consider the following frequency distribution:

Class Interval10-1515-2020-2525-3030-35
Frequency591268

The modal class is 10-15.
Reason : The class having maximum frequency is called the modal class.

(d) : Clearly, Reason is correct.
The maximum frequency is 12, which lies in the interval 20 – 25. So, the modal class is 20-25.
`\therefore` Assertion is wrong but Reason is correct.

Question.7.
Assertion : If for a certain frequency distribution, `l` = 24.5, `h` = 4, `f_{0}` = 14, `f_{1}` = 14, `f_{2}` = 15, then the value of mode is 25.
Reason : Mode of a frequency distribution is given by :
Mode = `l+\left(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\right)\times h`.

(d) : Clearly, Reason is wrong.
Now, it is given that `l` = 24.5, `h` = 4, `f_{0}` = 14, `f_{1}` = 14, `f_{2}` = 15
`\therefore` Mode = `24.5+\left(\frac{14-14}{28-14-15}\right)\times 4`
⇒ Mode = 24.5 + 0
⇒ Mode = 24.5
`\therefore` Assertion is wrong but Reason is correct. 

Question.8.
Assertion : Consider the following frequency distribution:

Class Interval0-44-88-1212-1616-20
Frequency6352010

The median class is 12-16.
Reason : Let n = `\sum f_{i}`. Then, the class whose cumulative frequency is just lesser than `\left(\frac{n}{2}\right)` is the median class.

(c) (c) : We know that, the class whose cumulative frequency is just greater than `\left(\frac{n}{2}\right)` is the median class.
So, Reason is wrong.
The cumulative frequency distribution table from the given data can be drawn as:

Class IntervalFrequencyCumulative Frequency
0-466
4-839
8-12514
12-162034
16-201044

Here, `n` = 44 ⇒ `\frac{n}{2}`= 22, which lies in the interval 12 – 16.
So, it is the median class.
`\therefore` Assertion is correct but Reason is wrong.

Question.9.
Assertion : If the median and mode of a frequency distribution are 8.9 and 9.2 respectively, then its mean is 9.
Reason : Mean, median and mode of a frequency distribution are related as:
mode = 3 median – 2 mean

(d) : Clearly, Reason is correct.
Using the relation given in Statement-II, we have
⇒ 2 Mean = 3 Median – Mode
⇒ 2 Mean = `3 \times 8.9 – 9.2`
⇒ 2 Mean = `26.7 – 9.2`
⇒ 2 Mean = 17.5
⇒ Mean = 8.75
`\therefore` Assertion is wrong but Reason is correct.

Question.10.
Assertion : The arithmetic mean of the following frequency distribution is 25.

Class Interval0-1010-2020-3030-4040-50
Frequency51815166

Reason : Mean`(\overline{x})=\frac{\sum f_{i}x_{i}}{\sum f_{i}}`, where `x_{i}` = `\frac{1}{2}`(Lower limit+Upper limit) of the `i^{th}` class interval and `f_{i}` is its frequency.

(a) : Clearly, Reason is correct.
Now, the frequency distribution table from the given data can be drawn as :

Class IntervalFrequency (`f_{i}`)`x_{i}``f_{i}x_{i}`
0-105525
10-201815270
20-301525375
30-401635560
40-50645270
 `\sum f_{i}`=60 `\sum f_{i}x_{i}`=1500

`\therefore` Mean = `\frac{\sum f_{i}x_{i}}{\sum f_{i}}`
⇒ Mean = `\frac{1500}{60}`
⇒ Mean = 25, which is true.
`\therefore` Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

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