# Mathematics Questions and Answers – Statistics – Mode of Grouped Data

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Statistics – Mode of Grouped Data”.

1. What is the mode in a data set?
a) The lowest number in a data set
b) The number that occurs less frequently
c) The number that occurs most frequently
d) The highest number in a data set

Explanation: The number which is occurred most frequently in a dataset is the mode in a data Set. A set of numbers can contain more than one Mode.

2. What is the mode of 8, 5, 7, 10, 15, 21, 5, 7, 2, 5?
a) 2
b) 5
c) 7
d) 21

Explanation: Mode in a data set is defined as the number that occurs most frequently in a data set.
5 occurred three times, 7 occurred two times, 2 and 21 occurred one time each.
5 is the most repeated number according to the definition mode.

3. Below are the results of the students in an exam. Find the mode of given results.
90, 80, 77, 86, 90, 91, 77, 25, 45, 35, 66, 69, 65, 43, 65, 75, 43, 90, 89.
a) 43
b) 77
c) 65
d) 90

Explanation: 90 occurred thrice. 77, 43 and 65 occurred twice.
In the above data set, 90 occurred three times and other numbers appeared once or twice. So, 90 is the mode of the above data set.
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4. Find the mode of given samples.
47, 25, 15, 89, 47, 89, 89, 1, 47, 73, 29, 64, 95, 90, 47, 25.
a) 85
b) 47
c) 25
d) No Mode

Explanation: 89 and 25 occurs twice, 64 occurs once, 47 occurs four times.
Since 47 has occurred four times in the above data set and other numbers less than that. The mode of the above data set is 47.

5. What is the mode of 19, 18, 9, 24, 1, 12, 23, 75?
a) 75
b) 1
c) 19
d) No mode

Explanation: According to the definition of mode, a mode is a number that occurs most frequently. There is no such number which is repeated more than once . So, we can say there is No Mode.

6. What is the mode of 20, 15, 13, 12, 9, 17, 13, 1, 9?
a) 13
b) 9
c) Both 13 and 19
d) No mode

Explanation: In the above data set, both 13 and 9 are repeated twice and a data set can have more than one mode. So, the mode is both 13 and 9.

7. Which of the following data sets have the highest Mode?
Data set 1: 11, 13, 14, 25, 30, 14, 14, 4.
Data set 2: 22, 12, 27, 22, 17, 4, 7, 13.
a) Data 1et 2
b) Data set 2
c) Both data sets
d) No mode

Explanation: The mode of the data set 1 is 14 which occurred thrice. The mode of the data set 2 is 22 which occurred twice and the question is which data set has the highest mode so, data set 2 is the answer.

8. The Values of mean and median are given as 22.5 and 20 respectively. Find the approximate value of Mode.
a) 15
b) 20
c) 12
d) 13.5

Explanation: The empirical mean median mode relation is given as
Mean – Mode = 3(Mean – Median)
Given Mean = 22.5 and Median = 20
22.5 – Mode = 3(22.5 – 20)
Mode = 15

9. Find the value of mode if the mean and median are 25 and 20 respectively.
a) 12
b) 18
c) 10
d) 17.5

Explanation: The empirical mean median mode relation is given as
Mean – Mode = 3(Mean – Median)
Given Mean = 25 and Median = 20
25 – Mode = 3(25 – 20)
Mode = 10

10. If the value of the mean is 10 and the median is 2 less than the mean. Find the Mode.
a) 2
b) 3
c) 4
d) 5

Explanation: The empirical mean median mode relation is given as
Mean – Mode = 3(Mean – Median)
Given Mean = 10 and Median = Mean – 2 = 10 – 2 = 8
10 – Mode = 3(10 – 8)
Mode = 4

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