If you truly think about it, you will realize that we all are constantly surrounded by numbers, aggregates, and statistics. For example, have you recently watched a cricket match and saw the run rate project on the screen? Or have you recently got the result of your examination and told your parents about your aggregate percentage?
As you might have guessed, in both of these cases, we are dealing with a collection of data that is highlighted by a single value. This is also known as statistics. And in this article, readers will be able to learn more about statistics, measures of central tendencies, and the difference between median and mode. We will look at the difference between mean and mode.
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Before we talk about the mean and mode difference, we need to have a grasp on the basics of this concept. As we mentioned above, statistics is a branch of mathematics that deals with the collection of information and data. The collection of information and data is done for a particular purpose.
For example, if there is a game of cricket and one wants to create a written record of each run for each ball, then that would give us the statistics of the game. A representation like this can be done in several ways, including graphs, tables, bar graphs, pie-charts, and pictorial representations.
Going in the same direction, it should be noted that statistics also consists of various important topics. The measure of central tendency is one such topic. To understand what measures of central tendencies mean, you need to know that in statistics we often tend to represent a set of data through a representation value.
The representation value would provide an approximate definition for the entire collection of data. And this value is known as the measure of central tendency. One should also remember that the measures of central tendency refer to values around which the entire collection of data is centered.
There are various parameters that are used for measures of central tendency. However, the most common parameters are:
We will learn more about these parameters in the next section of the article.
Let’s start our discussion by first understanding the meaning of mean. According to experts, the mean can be defined as the value of central tendency that represents the average of any given collection of data. Mean is also the most commonly used measure of central tendency.
It should be noted by students that mean is applicable for both discrete data and continuous data. Let’s take an example to further be familiar with this topic. Assume that there are n values in a set of data. These values are x1, x2, x3, x4, …, xn. This means that the mean of data can be given by:
x̅ = x1 + x2 + x3 + … + xn
This can also be represented by:
x̅ = ∑ni = 1 xin
In contrast, to the mean, the median can be defined as the mid-value of any given data set. The median value is only selected when the data is arranged in a particular order. The steps for finding the median value of a data set are mentioned below.
Arrange the data in ascending or descending order.
If the number of observations or values that are present in the data is odd, then the median value can be calculated by:
(n + ½)th observation
If the number of observations or values that are present in the data is even, then the median value can be calculated by:
(n/2)th and (n/2 + 1)th observation
Now, let’s talk about the mode. The mode can be described as the most frequently occurring number of a data set. For example, let’s consider a data set of marks that were obtained by various students in science. This data set is given below in the form of a table.
From this table, you must be able to observe that the maximum frequency observation is 73. This is because there are three students out of six students who have scored 73 marks. Hence, the mode for this data collection is 73.
Till now, we have looked at what statistics mean along with mean, median, and mode. Now, in this section, we will try to understand the differences that exist between mean, median, and mode. To make it easier for students to learn this topic, we have mentioned all the difference in the form of a table. And that table is mentioned below.
You know about the difference between mean, median, and mode. But did you know that all the three measures of central tendencies are related to one another? This is true and the mean, median, and mode are related to one another by the formula that is mentioned below.
Mode = 3 Median - 2 Mean
Also, according to this formula, the three measures of central tendencies are arranged in a moderately skewed distribution. This relation is also known as the empirical relationship. It is used for finding one of the measures when the value of the other two measures is already known for a data set.
This relationship can also be written in different forms by just interchanging the RHS and LHS. Also, did you know that in statistics, the range is explained as the difference between the highest and lowest data value in a set? The formula that one can use for calculating the range of a data set is mentioned below.
Range = Highest value - Lowest value
Question 1. Calculate the Values of Mean, Median, Mode, and Range for the Data set that is Given Below.
90, 94, 53, 68, 79, 94, 53, 65, 87, 90, 70, 69, 65, 89, 85, 53, 47, 61, 27, 80
Answer: We know that the given data set is 90, 94, 53, 68, 79, 94, 53, 65, 87, 90, 70, 69, 65, 89, 85, 53, 47, 61, 27, 80
This shows that the total number of observations is 20
This means that
Mean = (Sum of observations) / Number of observations
= (90 + 94 + 53 + 68 + 79 + 94 + 53 + 65 + 87 + 90 + 70 + 69 + 65 + 89 + 85 + 53 + 47 + 61 + 27 + 80) / 20
= 1419 / 20
The value of mean is 70.95
To find the value of median we have to arrange the data set in an ascending order. The observations in an ascending order are:
27, 47, 53, 53, 53, 61, 65, 65, 68, 69, 70, 79, 80, 85, 87, 89, 90, 90, 94, 94
Here, n = 20
Median = 1 / 2 [(n / 2) + (n / 2 + 1)]th observation
= 1 / 2 [10 + 11]th observation
= 1 / 2 (69 + 70)
= 139 / 2
Hence, the value of the median is 69.5
We know that mode is the most frequently occurring number in a given data set. This means that the value of mode for this data set is 53.
Range = highest value - lowest value
= 94 - 27
Range = 67
Question 2. Mention the Three Measures of Central Tendencies.
Answer: The three measures of central tendencies are:
Question 3. What do you Understand by the Mean in Statistics? Provide an Example with Your Answer.
Answer: Mean can be defined as the average of any given data set. The formula for calculating the value of the mean is mentioned below.
Mean = Total of observations / number of observations
For example, if a data set is 2, 5, 6, 7, 8, and we have to find the value of the mean, then we will follow the steps that are mentioned below.
Mean = (2 + 5 + 6 + 7 + 8) / 5
Mean = 28 / 5 = 5.6
Hence, the value of the mean is 5.6