Mean, Median and Mode

Central Tendency-

Central tendency does not depict any individual value of the data set. However, it gives the overall summary of the set of data. There are various uses of mean median and mode. We are going to discuss the uses of central tendency in daily life as well as the application of mean , median mode.

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Measures of Central Tendency:

The central tendency of any data set can be measured by anyone of the following ways.

• Mean

• Median

• Mode

Mean

We can define mean as the sum of all the values of the variable divided by the total number of values.

a\[_{m}\] = \[\frac{a_{1} + a_{2} +a_{3} + a_{4}}{4}\] = \[\frac{\sum_{0}^{n}a}{n}\]

Median

Median

The median of a set of data values can be defined as the middle value of the data set when all  the values have been arranged in ascending order.  

Median is calculated as

Where n is equal to the number of values in the data. If the number of values in the data set is even ( can be divided by 2), then the median is known to be the average of the two middle values.

Median = \[\frac{n}{2}\]th observation for odd number of observations

Mode

Mode of a statistical data is the value of that variable which has the maximum frequency.There are various different uses of mean,median mode in daily life.

Application of Mean, Median, Mode

Let’s Discuss the Applications of Mean, Median Mode 

1. Mean, median & mode shows different perspectives of  the similar data.

2. Mean basically gives us the average of the data. All data is given equal importance in this case. It is used in  the case where all data is important. For example:We can say the average salary of employees in an organization.

3. We use mode when we need to find the most frequent data. For example, suppose if we need to find the most favorite Subject of students in a given class, we can use mode.

Application of Median -

Let’s discuss the application of median-

1. Median can be used to find the middle most data. It can be used to determine a point from where 50% of data is more & 50% data is less. 

2. One more application of median is it is used where extreme cases can be ignored.For example,to find the performance of a cricketer where his worst  and best extreme performance can be ignored to give his consistent performance.

These are the few uses of mean, median and mode.

Uses of Central Tendency in Daily Life

There are various uses of central tendency in daily life. Let’s discuss the uses of central tendency in daily life- 

• Central tendency helps to compress a data set to a single value which represents all the values in the data. 

• It, therefore, helps to work with a larger set of grouped or ungrouped data.

• Central tendency also can be used in comparing one set of data with the other. It also helps in easier and effective pictorial representation of the given data set. 

• Central tendency in statistics can be used to compare a single value of data in a set of data with the other values in the data set. 

• Had it been we did not have the measures of central tendency, it would have been very difficult to perform statistical computations accurately. 

Solved Examples -

Example 1) Find the mean, median, mode, and range for the following list of values given below:

13, 18, 13, 13, 13, 16, 14, 21, 13

The mean is known as the usual average, so we will add and then divide the sum by the number of elements:

(13 + 18 + 13 + 13 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 14.8

Note that the mean, in this case, does not occur as any value from the original list.You should not assume that the mean of the given numbers will be one of your original numbers in the list.

The median is the middle value in the original list of numbers.

To find the median first we have to rewrite the list in numerical order:

13, 13, 13, 13, 13, 14, 16, 18, 21

We know that there are nine numbers in the original list, so the middle one in the original list will be the (9)/ 2 = 9 /2  that gives 4.5 that is the 5th number:

13, 13, 13, 13, 13, 14, 16, 18, 21

So the median is 13.

The mode can be defined as the number that is repeated more often than any other, so 13 is the mode from the original list.

The largest value in the original list is 21, and the smallest value in the original list is 13, so the range we get is 21 – 13 = 8.

Mean of the list    = 14.8

Median of the list = 14

Mode of the list    = 13

Range of the list   = 8

Note: The formula for the place to find the median in the original list is equal to "([the number of data points in the original list] + 1) ÷ 2", but you don’t need the formula.You can just count in from both ends of the original list until you meet in the middle, if you prefer, especially if your original list is short. Either way it will work.