# Problems on Median of Raw Data

Median is another measure of central tendency of a distribution. We will solve different types of problems on Median of Raw Data.

Solved Examples on Median of Raw Data:

1. The height (in cm) of 11 players of a team are as follows:

160, 158, 158, 159, 160, 160, 162, 165, 166, 167, 170.

Find the median height of the team.

Solution:

Arrange the variates in the ascending order, we get

157, 158, 158, 159, 160, 160, 162, 165, 166, 167, 170.

The number of variates = 11, which is odd.

Therefore, median = $$\frac{11 + 1}{2}$$th variate

= $$\frac{12}{2}$$th variate

= 6th variate

= 160.

2. Find the median of the first five odd integers. If the sixth odd integer is also included, find the difference of medians in the two cases.

Solution:

Writing the first five odd integers in ascending order, we get

1, 3, 5, 7, 9.

The number of variates = 5, which is odd.

Therefore, median = $$\frac{5 + 1}{2}$$th variate

= $$\frac{6}{2}$$th variate

= 3th variate

= 5.

When the sixth integer is included, we have (in ascending order)

1, 3, 5, 7, 9, 11.

Now, the number of variates = 6, which is even.

Therefore, median = mean of the $$\frac{6}{2}$$th and ($$\frac{6}{2}$$ + 1)th variate

= mean of the 3th and 4th variates

= mean of 5 and 7

= ($$\frac{5 + 7}{2}$$

= ($$\frac{12}{2}$$

= 6.

Therefore, the difference of medians in the two cases = 6 – 5 = 1.

3. If the median of 17, 13, 10, 15, x happens to be the integer x then find x.

Solution:

There are are five (odd) variates.

So, $$\frac{5 + 1}{2}$$th variate, i.e., 3rd variate when written in the ascending order will the medina x.

So, the variates in ascending order should be 10, 13, x, 15, 17.

Therefore, 13 < x < 15.

But x is an integer.

So, x = 14.

4. Find the median of the collection of the first seven whole numbers. If 9 is also included in the collection, find the difference of the medians in the two cases.

Solution:

The first seven whole numbers arranged in ascending order are

0, 1, 2, 3, 4, 5, 6.

Here, the total number of variates = 7, which is odd.

Therefore, $$\frac{7 + 1}{2}$$th, i.e., 4th variate is the median.

So, median = 3.

When 9 is included in the collection, the variates in the ascending order are

0, 1, 2, 3, 4, 5, 6, 9.

Here the number of variates = 8, which is even.

Therefore, median = mean of the $$\frac{8}{2}$$th variate and the ($$\frac{8}{2}$$ + 1)th variate

= Mean of the 4th variate and the 5th variate

= mean of 3 and 4

= $$\frac{3 + 4}{2}$$

= $$\frac{7}{2}$$

= 3.5.

Therefore, the difference of medians = 3.5 – 3 = 0.5

5. If the numbers 25, 22, 21, x + 6, x + 4, 9, 8, 6 are in order and their median is 16, find the value of x.

Solution:

Here, the number of variates = 8 (in descending order).

8 is even.

Therefore, median = mean of the $$\frac{8}{2}$$th variate and the ($$\frac{8}{2}$$ + 1)th variate

= Mean of the 4th variate and the 5th variate

= Mean of x + 6 and x + 4

= $$\frac{(x + 6) + (x + 4)}{2}$$

= $$\frac{x + 6 + x + 4}{2}$$

= $$\frac{2x + 10}{2}$$

= $$\frac{2(x + 5)}{2}$$

= x + 5.

According to the problem,

x + 5 = 16

⟹ x = 16 - 5

⟹ x = 11.

6. The marks obtained by 20 students in a class test are given below.

Marks Obtained

6

7

8

9

10

Number of Students

5

8

4

2

1

Find the median of marks obtained by the students.

Solution:

Arranging the variates in ascending order, we get

6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10.

The number of variates = 20, which is even.

Therefore, median = mean of $$\frac{20}{2}$$th and ($$\frac{20}{2}$$ + 1)th variate

= mean of the 10th and 11th variates

= mean of 7 and7

= ($$\frac{7 + 7}{2}$$

= ($$\frac{14}{2}$$

= 7.

## You might like these

• ### Worksheet on Estimating Median and the Quartiles using Ogive | Answers

In worksheet on estimating median and the quartiles using ogive we will solve various types of practice questions on measures of central tendency. Here you will get 4 different types of questions on estimating median and the quartiles using ogive.1.Using the data given below

• ### Worksheet on Finding the Quartiles & Interquartile Range of Raw Data

In worksheet on finding the quartiles and the interquartile range of raw and arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the quartiles and the interquartile

• ### Worksheet on Finding the Median of Arrayed Data | Hint | Answers

In worksheet on finding the median of arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the median of arrayed data. 1. Find the median of the following frequency

• ### Estimate Median, Quartiles from Ogive | Frequency Distribution

For a frequency distribution, the median and quartiles can be obtained by drawing the ogive of the distribution. Follow these steps. Step I: Change the frequency distribution into a continuous distribution by taking overlapping intervals. Let N be the total frequency.

• ### Worksheet on Finding the Median of Raw Data | Find the Median |Answers

In worksheet on finding the median of raw data we will solve various types of practice questions on measures of central tendency. Here you will get 9 different types of questions on finding the median of raw data. 1. Find the median. (i) 23, 6, 10, 4, 17, 1, 3 (ii) 1, 2, 3

• ### Median Class | continuous distribution | Cumulative Frequency

If in a continuous distribution the total frequency be N then the class interval whose cumulative frequency is just greater than $$\frac{N}{2}$$ (or equal to $$\frac{N}{2}$$) is called the median class. In other words, median class is the class interval in which the median

• ### Range & Interquartile Range |Measures of Dispersion|Semi-interquartile

The variates of a data are real numbers (usually integers). So, thay are scattered over a part of the number line. An investigator will always like to know the nature of the scattering of the variates. The arithmetic numbers associated with distributions to show the nature

• ### Find the Quartiles for Arrayed Data | Lower Quartiles |Upper Quartiles

Here we will learn how to find the quartiles for arrayed data. Step I: Arrange the grouped data in ascending order and from a frequency table. Step II: Prepare a cumulative-frequency table of the data. Step III:(i) For Q1: Select the cumulative frequency that is just greater

• ### Upper Quartile and the Method of Finding it for Raw Data |3rd Quartile

If the data are arranged in ascending or descending order then the variate lying at the middle between the largest and the median is called the upper quartile (or the third quartile), and it denoted by Q3. In order to calculate the upper quartile of raw data, follow these

• ### Lower Quartile and the Method of Finding it for Raw Data | Definition

The three variates which divide the data of a distribution in four equal parts (quarters) are called quartiles. As such, the median is the second quartile. Lower quartile and the method of finding it for raw data: If the data are arranged in ascending or descending order

• ### Finding the Median of Grouped Data | Median of Arrayed Data | Examples

To find the median of arrayed (grouped) data we need to follow the following steps: Step I: Arrange the grouped data in ascending or descending order, and form a frequency table. Step II: Prepare a cumulative-frequency table of the data. Step III: Select the cumulative

• ### Median of Raw Data |The Median of a Set of Data|How to Calculate Mean?

The median of raw data is the number which divides the observations when arranged in an order (ascending or descending) in two equal parts. Method of finding median Take the following steps to find the median of raw data. Step I: Arrange the raw data in ascending

• ### Worksheet on Finding the Mean of Classified Data | Find the Mean | Ans

In worksheet on finding the mean of classified data we will solve various types of practice questions on measures of central tendency. Here you will get 9 different types of questions on finding the mean of classified data 1.The following table gives marks scored by students

• ### Worksheet on Finding the Mean of Arrayed Data | Calculate the Mean

In worksheet on finding the mean of arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 12 different types of questions on finding the mean of arrayed data.

• ### Worksheet on Finding the Mean of Raw Data | Mean of Raw Data | Answers

In worksheet on finding the mean of raw data we will solve various types of practice questions on measures of central tendency. Here you will get 12 different types of questions on finding the mean of raw data. 1. Find the mean of the first five natural numbers. 2. Find the

• ### Step-deviation Method | Formula for Finding the Mean by Step-deviation

Here we will learn the Step-deviation method for finding the mean of classified data. We know that the direct method of finding the mean of classified data gives Mean A = $$\frac{\sum m_{i}f_{i}}{\sum f_{i}}$$ where m1, m2, m3, m4, ……, mn are the class marks of the class

• ### Finding the Mean from Graphical Representation | Solved Example

Here we will learn how to find the mean from graphical representation. The ogive of the distribution of marks of 45 students is given below. Find the mean of the distribution. Solution: The cumulative-frequency table is as given below. Writing in overlapping class intervals

• ### Mean of Classified Data (Continuous & Discontinuous)|Formula| Examples

Here we will learn how to find the mean of classified data (continuous & discontinuous). If the class marks of the class intervals be m1, m2, m3, m4, ……, mn and the frequencies of the corresponding classes be f1, f2, f3, f4, .., fn then the mean of the distribution is given

• ### Mean of Ungrouped Data | Mean Of Raw Data | Solved Examples on Mean

The mean of data indicate how the data are distributed around the central part of the distribution. That is why the arithmetic numbers are also known as measures of central tendencies. Mean Of Raw Data: The mean (or arithmetic mean) of n observations (variates)

• ### Mean of Grouped Data|Mean Of Arrayed Data|Formula for Finding the Mean

If the values of the variable (i.e., observations or variates) be x$$_{1}$$, x$$_{2}$$, x$$_{3}$$, x$$_{4}$$, ....., x$$_{n}$$ and their corresponding frequencies are f$$_{1}$$, f$$_{2}$$, f$$_{3}$$, f$$_{4}$$, ....., f$$_{n}$$ then the mean of the data is given by