Median Questions

The median questions and answers are provided here to help students grasp the concept fast. One of the most fundamental topics taught in primary and secondary classes is median. The NCERT curriculum is used to frame the questions. Students can refer to these questions to get a fast review of the concepts, and can practise them to become more acquainted with the topics. Check your answers referring to the comprehensive explanations given for each question. Click here to know more about Median.

Go through the median questions and answers below and practise them.

Median Questions with Solutions

1. How to find the median?

Solution:

The steps to find the median are as follows:

Step 1: Arrange the given data in ascending order.

Step 2: Count the number of observations (n) to check whether it is odd or even.

Step 3: If the number of observations (n) is odd, use the formula [(n +1)/2]^th term to find the median.

Step 4: If the number of observations (n) is even, use the formula [(n/2)^th term + ((n/2) + 1)^th term]/2 to find the median value.

Also, read: How to Find Median

2. The runs scored by 11 players in the cricket match are as follows:

7, 16, 121, 51, 101, 81, 1, 16, 9, 11, 16

Find the median of the data.

Solution:

Given data: 7, 16, 121, 51, 101, 81, 1, 16, 9, 11, 16.

Now, arrange the data in ascending order, we get

1, 7, 9, 11, 16, 16, 16, 51, 81, 101, 121.

Here, the number of observations is 11, which is odd.

Thus, median = 6th term

Hence, the median of the given data is 16.

3. Find the median for the data 8, 5, 7, 10, 15, 21.

Solution:

Arranging the given data in ascending order, we get,

5, 7, 8, 10, 15, 21.

Here, the number of observations is 6, which is even.

Hence, Median = [(n/2)^th term + ((n/2) + 1)^th term]/2

Median = [(6/2)^th term + ((6/2) + 1)^th term]/2

Median = (3rd term + 4 term )/2

Here, 3rd term = 8 and 4th term = 10

Therefore, median = (8+10)/2 = 18/2 = 9

Hence, the median of the given data is 9.

4. What is the relation between mean, median and mode?

Solution:

The relation between mean, median and mode is (Mean – Median) = 1/3 (Mean – Mode).

This can also be written as follows:

3 (Mean – Median) = (Mean – Mode)

3 Mean – 3 Median = Mean – Mode

3 Median = 3 Mean – Mean + Mode

3 Median = 2 Mean + Mode

Also, read: Relationship between Mean, Median and Mode.

5. For a moderately skewed distribution, mean = 12 and mode = 6. Using these values, find the value of the median.

Solution:

Given that, mean = 12 and mode = 6

We know that, 3 Median = 2 Mean + Mode

Now, substitute the values in the formula, we get

3 Median = 2(12) + 6

3 Median = 24 + 6

3 Median = 30

Median = 30/3 = 10.

Hence, the value of median is 10.

6. What is the median of two numbers?

Solution:

For a set of two numbers, the value of the median will be the same as the value of the mean.

For example, 2 and 10 are the two numbers.

Here, median = (2+10)/2 = 12/2 = 6

Also, mean = (2+10)/2 = 12/2 = 6.

Hence, the median of two numbers is equal to the mean.

7. Find the median of the first 5 whole numbers.

Solution:

The first 5 whole numbers are 0, 1, 2, 3, 4.

Here, the number of observations is 5. So, the 3rd term is the middle term, which is 2.

Hence, the median of the first 5 whole numbers is 2.

8. What is the median of 4, 2, 7, 3, 10, 9, 13?

Solution:

Given data: 4, 2, 7, 3, 10, 9, 13

First, arrange the given data in ascending order.

I.e., 2, 3, 4, 7, 9, 10, 13

So, the number of observations is 7. (n= 7)

Since the number of observations is odd, the median can be calculated as follows:

Median = [(n +1)/2]^th term

Median = [(7 +1)/2]^th term

Median = [(8)/2]^th term

Median = 4^th term = 7

Hence, the median of 4, 2, 7, 3, 10, 9, 13 is 7.

9. The marks scored by a student in different subjects are 45, 91, 62, 71, 55. Find the median of the given data using the median formula.

Solution:

Given data: 45, 91, 62, 71, 55

Arranging the given set in ascending order, we get 45, 55, 62, 71, 91.

Here, we have an odd number of observations. (i.e.) 5.

If “n” is odd, the median formula is [(n +1)/2]^th term

= [(5 +1)/2]^th term

=[(6)/2]^th term = 3rd term = 62.

Hence, the median of the given data is 62.

10. The weight of 8 students in kgs are 54, 49, 51, 58, 61, 52, 54, 60. Find the median weight.

Solution:

Given data: 54, 49, 51, 58, 61, 52, 54, 60.

Arranging the data in ascending order, we get 49, 51, 52, 54, 54, 58, 60, 61.

Here, n = 8.

Therefore, the middle two terms are 54 and 54.

Hence, median = (54 + 54)/2 = 108/2 = 54.

Therefore, the median weight is 54 kg.

Video Lesson on Median of Data

Practice Questions

1. Find the median of the first five natural numbers.
2. Find the median of the data 130, 123, 146, 109, 112, 111.
3. Find the median of the first 10 composite numbers.

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