# How to Calculate Mean, Median, and Mode? Statistics(Central Tendency) ## How to Calculate the Mean, Median, and Mode? Statistics(Central Tendency)

In this article, we will discuss Chapter 14 Statistics- Mean, Median, and Mode out for Class 10 Maths. For online CBSE Class, 10 Maths classes kindly visit our website. www.takshilalearning.com

Central Tendency

It is a measure that tells us where the middle of a bunch of data lies.

The 3 most common measures of central tendency are the mean, the median, and the mode. Let’s take a situation where Mary & Hari got marks for 5 questions. Both of them claim to have performed better. Let’s see who has performed better in the exam.

Mean: Let’s find the average scores.

1. Average Score of Mary is (10+8+9+8+7)/5  =8.4
2. Average Score of Hari is (4+7+10+10+10)/5 = 8.2

Based on the Mean data, Mary has performed better.

The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations. It is denoted by ‘bar’.

All data is given equal importance in Mean, the extreme values are not ignored. For Ungrouped data,

Median: Let’s arrange their score in ascending order in the blue table. Now we will take the middlemost score. Since we are talking about the central tendency of data, the middlemost score should also reflect the central tendency of data. The middlemost score for May is 8, while that of Hari is 10.

So based on middle score or median data, Hari has performed better.

When the number of observations (n) is odd, the median is the value of the ((n+1)/2) Th observation.

When the number of observations (n) is even, the median is the mean of (n/2) & (n/2 + 1) Th observations.

Median Ignores extreme values &Tells the point from where 50% data is lesser and 50% data is more

Understand and practice Mean, Median, and Mode with animated videos and digital worksheets and games. Mode: Let’s check the most frequent score. Based on the most often score, 8 is the most often score( 2 times) for Mary & 10 is the most often score ( 3 times) for Hari. Going with the most often score or Mode, Hari has performed better.

The mode is that value of the observation which occurs most frequently, i.e., an observation with the maximum frequency is called the mode. E.g. it can be used to find the which is the most favorite subject of a class. Numerical: In a mathematics test given to 15 students, following marks are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60. Find the mean, median and mode of this data.

Mean is average data, the Median is middlemost data & Mode is the most frequent data.

Mean = Sum of all observations/number of observations

= (41+ 39+ 48+ 52+ 46+ 62+ 54+ 40+ 96+ 52+ 98+ 40+ 42+ 52+ 60 ) / 15

= 822/15

= 54.8

To find middlemost data, we have to arrange data in ascending order & then find middlemost.

Data in ascending order: 39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98.

Middlemost data, in this case, is 52 & thus Median is 52.

Also, we see that the most frequent data is 52 & thus mode is 52.

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