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.
Mean:
It is the average of all the values of a dataset.
Significance: While buying a car you are not interested in the no. of Kilometers car ran in each liter of petrol but the average of all the figures
Example: Find out the average of car based on following figures
Litre | Kms |
First | 20 |
Second | 18 |
Third | 21 |
Fourth | 21 |
Fifth | 20 |
Mean or Average = Sum of dataset values /No. of dataset values
Mean = (20 + 18 + 21 + 21 + 20) / 5
Mean = 100 / 5
Mean = 20 km/l
Inference: So car may have ran different kilometers in each liter of petrol but the average is 20 kilometer per liter.
Median
It gives the middle no. of any dataset.
Significance: It provides an indication towards the center of dataset, it is actually a value which has equal no. of data figures on both of its sides in the given dataset. It also has huge importance and it not necessarily be equal to mean or average
Example: Find out the median age of television viewers based on following ages (6, 8, 9, 6, 86)
Median is the middle no. of a sorted dataset so first sorting the dataset in ascending order
Sorted dataset : (6, 6, 8, 9, 86)
As there are 5 values, so value at third position is Median,
So, Median = 8
Let us compare it with the Mean
Mean = (6 + 6 + 8 + 9 + 86) / 5
Mean = 23
Inference: Though Mean is 23 but Median is 8 and maximum people will watch television if we have channel which is for 8 years old and not 23
Mode
It gives the most often occurring figure of any dataset, basically the no. which has occurred maximum times in given dataset is the Mode of that dataset, in case when there is no reoccurrence then there is No Mode in that dataset
Significance: It provides the figure which has highest frequency in any given dataset
Example: Find out the T-Shirt size which should be produced to make best sales among following given T-Shirt sizes (40, 42, 42, 42, 44, 44, 46, 50, 50, 50, 50, 50)
Size | Occurrence |
40 | 1 |
42 | 3 |
44 | 2 |
46 | 1 |
50 | 5 |
Mode is the no. which occurred most often, so Mode= 50
Where as:
Mean = 45.83
Median = 45
Inference: Though Mean is 45.83 and Median is 45 but maximum people who may buy t-shirt wears size of 52, so here Mode helps us in making decisions.
Range
It gives the coverage or span in which data in dataset is spread
Significance: It provides the difference between the highest and lowest value in any given dataset
Example: Find out the Range of ages available in following dataset (6, 9, 10, 7, 11)
Range is the difference between the highest and lowest values.
So, Range = 11 – 6
Range = 5
Inference: It gives the span of values the dataset is covering in it.
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] |
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Options | A) 7 correct answer B) 9 C) 4 D) 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 = 7^{th} 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 | A) 5.5 B) 8 correct answer C) 8.5 D) 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 | A) 12 B) 13 C) 10 correct answer D) 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 | 10.58.88.5 correct answer10.3 |
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 = 8Mean 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 | A) 4 correct answer B) 5 C) 2 D) 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 |