Mathematics: Mean, Median, Mode & Range

The terms mean, median and mode are used to describe the central tendency of a large data set. Range provides provides context for the mean, median and mode.

Question / Answer

Question #1 The mean of mode, median and range of the data :

2, 1, 2, 3, 3, 6, 4, 8, 14, 9, 4, 8, 4 is :

[Mathematics] [CTET-2016-09]
Options
  • correct answer
  • 9
  • 4
  • 6
Answer Explanation Given that,  The mean of mode, median and range of the data
= 2, 1, 2, 3, 3, 6, 4, 8, 14, 9, 4, 8, 4
Range = 14 – 1 = 13
Mode = 4
Median  = 7th term = 4
Mean      = 7
Question #2 The mean of median and mode of the data 7, 6, 7, 9, 8, 8, 10, 8 is

[Mathematics] [CTET-2014-02]
Options
  • 5.5
  • correct answer
  • 8.5
  • 9
Answer Explanation Arranging the above data in ascending order we get
6,7,7,8,8,8,9,10
Median for even number of observation is the mean of the n/2 – 1 and he n/2 +1 value.
Here, n=10 => mean of 4th and 5th value 0r (8+8)/2 = 8 is the median of the above observation.
Mode is the observation that is repeated most time. here it is 8.There mean of mode and median = ( 8 + 8)/2 = 8
Question #3 The sum of mean, mode and median of the data 6, 3, 9, 5, 1, 2, 3, 6, 5, 1, 3 is

[Mathematics] [CTET-2015-09]
Options
  • 12
  • 13
  • 10 correct answer
  • 11
Answer Explanation Mean = (6+3+9+1+2+3+6+5+1+3)/11 = 44/11 = 4
Mode = 3 (Most repeated number)
Median = middle value of  (1,1,2,3,3,3,5,5,6,6,9) = 3
And therefore their sum is 10.
Question #4 The mean of the median, mode and range the observations 6,6,9,14,8,9,9,8 is

[Mathematics] [CTET-2012-01]
Options
  • 10.5
  • 8.8
  • 8.5 correct answer
  • 10.3
Answer Explanation             Sorted dataset = (6, 6, 8, 8, 9, 9, 9, 14)

Median = Ave of middle values (8+9)/2 = 8.5
Mode = 9 (Most repeated number)
Range = 14 – 6 = 8

Mean of the median, mode and range = (8.5+9+8)/3 = 8.5

Question #5 The mean of range, mode and median of the data
4, 3, 2, 2, 7, 2, 2, 0, 3, 4, 4 is

[Mathematics] [CTET-2015-02]
Options
  • correct answer
  • 5
  • 2
  • 3
Answer Explanation Mean = sum of all number/(number of number)

The range of the above number is (largest number – smallest number) = 7-0 = 7
The mode of the above series is 2 (mode is the number that is repeated the most )

And the median is the number that lies exactly in the middle for a series with odd number of elements when arranged in increasing order.
0,2,2,2,2,3,3,4,4,4,7
(11 numbers in all. the number lying in the 6th place is the median )

Here the number is 3
Therefore the mean of range, mode and median is = (7+3+2)/3 = 12/3 = 4

Question #6 The median of 7,8,9,10,11,12 is

[Child Development and Pedagogy] [UPTET-2017-10]
Options
  • 8
  • 9
  • 5
  • 10 correct answer
Question #7 Ten observation 5, 9, 14, 15, x+ 1, 2x -13, 28, 30, 32, 34, are written in ascending order. The median of the data is 24 find the value of x.

[Mathematics] [UPTET-2017-10]
Options
  • 20 correct answer
  • 19
  • 21
  • 16
Answer Explanation No of observations = 10
As the No of observations is even ,
Median = [( n/2th observation) + (n/2)+1 th observation] ÷ 2
n/2 th observation = 5 th observation = x+1
(n/2)+1 th observation = 6th observation = 2 x-13
[x+1 + 2x -13] ÷ 2 = median
[x+1 + 2x -13] ÷ 2 = 24
(3x – 12) ÷ 2 = 24
3x – 12 = 24 × 2
3x – 12 = 48
3x = 48 + 12
3x =  60
x = 60 ÷ 3
x = 20
Question #8 Out of observation arranged in ascending order. the sixth and seventh observations are 14 and 15 respectively. Find the median of all the 12 observations.

[Mathematics] [UPTET-2016-12]
Options
  • 29
  • 14.5 correct answer
  • 15
  • None of these
Question #9 What is the median value of the following data ?

18, 26, 15, 20, 23, 15, 9, 21, 12, 24

[Child Development and Pedagogy] [OTET-2018-12]
Options
  • 19
  • 18 correct answer
  • 17
  • 15
Question #10 What is the median of the following scores ?

3, 5, 4, 9, 8

[Child Development and Pedagogy] [OTET-2017-09]
Options
  • 4
  • 3
  • correct answer
  • 8

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