RS Aggarwal Solutions Class 7 Chapter-21 Collection and Organisation of Data (Mean, Median and Mode) (Ex 21B) Exercise 21.2

This chapter focuses on the concept of mean, median and mode and their application. As we have discussed in the previous chapters, a class is considered a data set. In this chapter we will discuss in detail the definition, properties and application of mean, median and mode. In this context, ‘data’ means computer-stored information. The term ‘mean’, ‘median’ and ‘mode’ are used for the same meaning as in the English Language.

Mean:

Average of a collection of data. The average is calculated by counting the data elements and dividing the count by the number of data elements (say N)

E.g. In the collection of 100 data elements, say if 60 data elements are odd and 40 in even numbers, then the mean value is 60/100 = 0.6 = 60%.

Median:

Median is the middle number in a sorted collection of data

e.g. In the collection of 100 data elements, say if 50 data elements are in odd and 50 in even numbers, then the median value is 50/100 = 0.5 = 50%.

Mode:

Mode is the most frequent data element

e.g. In the collection of 100 data elements, say if 60 data elements are in odd and 40 in even numbers, then the mode value is even numbers = 60/100 = 0.6 = 60%.

The most commonly used way of calculating the means, median and mode is to take the arithmetic mean or “avg”, and median of the data. We would use the average mean rather than the mode. If the data is normally distributed, then these mean, median and mode are representative of the population. If the data is not normally distributed, these mean, median and mode do not represent the population. 

For instance, imagine we have a set of numbers like (1,2,3,4,5,6,7,8,9,10), it is clearly a very large set, but what would be the mode, median and mean? You would get 9.6, 4.3, and 9.4, but those numbers may not reflect the distribution of the numbers. They represent the most frequent number in the sample, which may be different from what is the mode, median or mean of the real numbers.

The concept of “mean, median, and mode” in statistics

In statistics, mean, median, and mode are basic statistical concepts, and statistics textbooks often present data in this manner. There are many other statistics concepts, such as frequency, variance, quantiles, and so on, but these three concepts are the most basic, and statistics textbooks tend to use these three statistics terms frequently.

Let’s look at this concept in more detail. First, we should understand what “mean,” “median” and “mode” mean. Mean refers to the average. If you have ten students, and the first student’s age is 20, then the mean age is 20, the second student’s age is 18, and so on. A student’s age is 20.5, but its mean is 20.

The median (or midpoint) is a concept in statistics. If you have ten students, and the first student’s age is 20, then the middle student’s age is 20, the second student’s age is 19, and so on. A student’s age is 20.5, but its median is 20.

In statistics, we always use the median, and not the average. The mode refers to the most common data value. In statistics, we use the term “mode” if a data value occurs most frequently.

Mean, median, and mode are concepts that can be calculated in various ways. The simplest way is to calculate the number of data values in a dataset, find the mean, median, or mode, and then divide by the total number of data values. This gives the mean, median, or mode. You can see an example of this in the screenshot below.

Other methods of calculating the mean, median, and mode are called “averages.” Let’s use this method to calculate the mean of our “age” data set. Here’s what we’ll do. First, we will get our five data values, and divide them by the total number of data values.

If we were doing the mean calculation, we would have used the formula:

5/10 = 0.5 = 5/10

For the median, we would use the formula:

4/9 = 0.44444 = 4/9

If we were calculating the mode, we would use the formula:

4/9 = 0.44444 = 4/9