Mean, median and mode of grouped and ungrouped data — practice questions

Question 1 · difficulty L2 · understanding

Consider the following frequency distribution : Class : 10-20 20-30 30-40 40-50 50-60 Frequency : $$\alpha$$ 110 54 30 $$\beta$$ If the sum of all frequencies is 584 and median is 45, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to _______________.

Question 2 · difficulty L2 · understanding

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is _________.

Question 3 · difficulty L2 · understanding

If the mean of the data Class 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 2 k 28 54 k + 1 5 is 21, then $k$ is one of the roots of the equation:

• A. $2x^2 - 23x - 10 = 0$
• B. $4x^2 - 35x + 24 = 0$
• C. $2x^2 - 19x - 10 = 0$
• D. $2x^2 - 35x + 98 = 0$

Question 4 · difficulty L2 · understanding

Let M denote the median of the following frequency distribution Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 3 9 10 8 6 Then 20M is equal to :

• A. 104
• B. 52
• C. 208
• D. 416

Question 5 · difficulty L3 · understanding

The mean of 10 numbers 7 $$\times$$ 8, 10 $$\times$$ 10, 13 $$\times$$ 12, 16 $$\times$$ 14, ....... is ____________.

Question 6 · difficulty L3 · understanding

Consider the following frequency distribution : Class : 0-6 6-12 12-18 18-24 24-30 Frequency : $$a$$ $$b$$ 12 9 5 If mean = $${{309} \over {22}}$$ and median = 14, then the value (a $$-$$ b) 2 is equal to _____________.

Question 7 · difficulty L3 · understanding

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18 , then the total number of students is :

• A. 52
• B. 44
• C. 40
• D. 48

Question 8 · difficulty L4 · understanding

Let $$x_{1}, x_{2}, x_{3}, \ldots, x_{20}$$ be in geometric progression with $$x_{1}=3$$ and the common ratio $$\frac{1}{2}$$. A new data is constructed replacing each $$x_{i}$$ by $$\left(x_{i}-i\right)^{2}$$. If $$\bar{x}$$ is the mean of new data, then the greatest integer less than or equal to $$\bar{x}$$ is ____________.

Question 9 · difficulty L4 · understanding

A variable $X$ takes values $0,0,2,6,12,20, \ldots, n(n-1)$ with frequencies ${ }^n C_0,{ }^n C_1,{ }^n C_2,{ }^n C_3,{ }^n C_4,{ }^n C_5, \ldots,{ }^n C_n$, respectively. If the mean of this data is 60 , then its median is :

• A. 56
• B. 42
• C. 72
• D. 90