RS Aggarwal Solutions Class 10 Chapter 9 - Mean, Median & Mode (Ex 9A) Exercise 9.1

RS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 9 - Mean, Median & Mode (Ex 9A) Exercise 9.1

RS Aggarwal Solutions Class 10 Chapter 9 - Mean, Median & Mode (Ex 9A) Exercise 9.1 - Free PDF

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Mean, Median and Mode

In statistics, the three measures of central tendency are Mean, Median, and Mode. While describing a set of data, we identify the central position of any data set. This is referred to as the central tendency measure. Every day, we come across data. We find them in newspapers, articles, bank statements, and phone and electricity bills, among other places. The question now is whether we can deduce some key characteristics of the data by examining only a subset of the data. The use of measures of central tendency or averages, such as Mean, Median, and Mode, makes this possible.

In the following sections, we'll look at Mean, Median, and Mode in greater depth using solved examples.

Mean

The sum of all observations divided by the number of observations is the even though Arithmetic Mean of a set of data. For instance, a team's five test scores are as follows: 257, 350, 392, 458 and 213 We use the Mean formula to calculate the Arithmetic Mean of data to find the team’s average score in a match:

The Mean is the sum of all observations divided by the number of observations.

Mean= (257 + 350 + 392 + 458 + 213)/5

Mean= 1670/5

= 334

X̄ denotes Mean and is pronounced as X bar.

Median

The data's Median is the value of the middle observation obtained after sorting the data in ascending order.

Consider the following information: 8, 2, 4, 7, 3,10, 9. Let's put this information in ascending order: 2, 3, 4, 7, 8, 9,10 There are seven observations in total. As a result, the Median is equal to the middle value, which is 7. This is what we can see: 2, 3, 4, 7, 8, 9,10 (As a result, 7 is the Median).

Mode

A Mode of data is the value that appears the most frequently in the given data, i.e. the observation with the highest frequency.

For instance, in a given data of 8 numbers, 6, 5, 2, 7, 8, 2, 6, 2, the number 2 is repeated for the maximum time which is thrice. Hence, 2 is the Mode in the data.

Mode= 2

FAQs on RS Aggarwal Solutions Class 10 Chapter 9 - Mean, Median & Mode (Ex 9A) Exercise 9.1

1. Is there any relation between the three measures of central tendencies, i.e., Mean, Median, and Mode?

The following relationships link the three, Mean, Median, and Mode (empirical relationship).

3Median = 2Mean + Mode

For instance, if we are asked to find the Mean, Median, and Mode of continuous grouped data, we can use the formulas discussed in the previous sections to find the Mean and Median, then use the empirical relation to find the Mode.

We have data with a Mode of 40 and a Median of 50, for instance.

Then, using the above Mean, Median, and Mode relationship, we can find the Mean.

∴2Mean = 3 × 50 - 40

∴2Mean = 110

⇒ Mean = 110/2

⇒ Mean = 55

2. Can Mean be differentiated from the average?

In everyday life, the term average is frequently used to denote a value that is typical of a group of quantities.

Despite the fact that average and Mean are not the same, most people use them interchangeably.

The average value denotes what is most likely to be expected.
They aid in the consolidation of large amounts of data into a single value.

With the values of the observations arranged in ascending order of magnitude, an average tends to lie in the middle. As a result, we call an average measure of the data's central tendency.

3. How do you distinguish between Mean and Median?

The mathematical average is known as the Mean, whereas the positional average is known as the Median.

Basis of Differentiation	Mean	Median
Definition	The average of the data provided (Mathematical Average)	Data has a central value (Positional Average)
Calculation	Divide the total number of observations by the sum of all values.	Arrange the data in ascending/descending order to find the Median value.
Data Values	For calculations, each value is taken into account.	Every value is not taken into account.
Effects at the Extremes	Extreme points have a big impact.	Extreme points do not affect it.

4. For ungrouped data, what are the formulas for finding the Mean, Median, and Mode mentioned in RS Aggarwal Solutions Class 10 Chapter 9 - Mean, Median & Mode (Ex 9A) Exercise 9?

Depending on whether the data is grouped or ungrouped, different sets of formulas can be used to find the Mean, Median, and Mode. For ungrouped data, the following formulas can be used to calculate the Mean, Median, and Mode:

Mean= Sum of all observations/Number of observations
Median= (n + 1)/2^nd observation if n is an odd number. If n is an even number, [(n/2)^{^th}obs.+ ((n/2) + 1)^th obs.]/2
Mode= Observation with the highest frequency is referred to as Mode.

5. What points are distinct between Mean, Median, and Mode according to RS Aggarwal Solutions Class 10 Chapter 9 - Mean, Median & Mode (Ex 9A) Exercise 9?

The average of the given sets of numbers is called the Mean. Add the numbers together, then divide the total by the number of observations.
To find the Mode, we look for numbers that appear more than once. The most frequently occurring number in the data is the Mode. There could be more than one Mode if there are other numbers that repeat to the same level. However, the Mean of a set of data is unique.
The Median is the value of the middlemost observation after the data has been arranged in ascending order.