# Mathematics Questions and Answers – Measures of Central Tendency

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Measures of Central Tendency”.

1. From the table given below, what is mean of marks obtained by 20 students?

Marks xi No. of Students fi
3 1
4 2
5 2
6 4
7 5
8 3
9 2
10 1
Total 20

a) 6.9
b) 5.8
c) 6.6
d) 6

Explanation: Mean of the marks can be found out by following way.

Marks xi No. of Students fi fi xi
3 1 3
4 2 8
5 2 10
6 4 24
7 5 35
8 3 24
9 2 18
10 1 10
Total $$\sum f_i=20$$ $$\sum_{i=1}^8 f_i x_i=132$$

We know that mean $$\bar{\bar{x}} = \frac{∑_{i=1}^8 f_i x_i}{\sum f_i} = \frac{132}{20}$$ = 6.6

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2. Height of 7 students (in cm) is given below. If the mean of height of 7 students is 165, what is the value of x?

168  170  x  160  162  164  162


a) 170
b) 165
c) 160
d) 169

Explanation: We know that mean = $$\frac{Sum \,of \,all \,observations}{Number \,of \,observations}$$
165 = $$\frac{168+170+x+160+162+164+162}{7}$$
1155 = 986 + x
Therefore, x = 169.

3. From the following data, what is the value of the median?

20  21  25  26  23  29  32  39  33


a) 26
b) 23
c) 25.22
d) 29

Explanation: If data contains n values and n is odd number, then median is the $$(\frac{n+1}{2})^{th}$$ observation after arranging them in either ascending or descending order.
Hence first, we will arrange the observations in ascending order:
20 21 23 25 26 29 32 33 39
Now, we can see that number of observations are nine, which is odd.
Hence median = $$(\frac{n+1}{2})^{th}$$ th observation = (9+1)/2
= 10/2
= 5th observation
Which is 26.

4. Observe the following observations. They are runs scored by a batsman in six matches and arranged in ascending order. If the value of median is equal to 54, then what is the value of x?

25  38  50  x  84  106


a) 60
b) 58
c) 54
d) 59

Explanation: Here, the number of observations are even (six).
Hence, median = $$\frac{n/2 \,th \,observation + (n/2+1)th \,observation}{2}$$
Where, n = no. of observation
Median = $$\frac{6/2 th \,observation + (6/2+1)th \,observation}{2}$$
= $$\frac{3^{rd} \,observation + 4^{th} \,observation}{2}$$
54 = $$\frac{50+x}{2}$$
108 = 50 + x
Hence, x = 58.

5. Below are the observations of the marks of a student. What is the value of mode?

84  85  89  92  93  89  87  89  92


a) 92
b) 9
c) 93
d) 89

Explanation: Mode is the value of the observation which occurs too frequently or frequency of which is highest.
We can see in the given observations that 89 has the highest frequency (3) or in other words, it occurs three times.
Hence, the value of mode is 89.

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