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