**Finding Median for Grouped Data**

Here we are going to see some practice questions on finding median for grouped data.

Median is the value which occupies the middle position when all the observations are arranged in an ascending or descending order. It is a positional average.

(i) Construct the cumulative frequency distribution.

(ii) Find (N/2)^{th} term

(iii) The class that contains the cumulative frequency N/2 is called the median class.

(iv) Find the median by using the formula:

Where l = Lower limit of the median class,

f = Frequency of the median class

c = Width of the median class,

N = The total frequency (∑f)

m = cumulative frequency of the class preceeding the median class

**Question 1 :**

A researcher studying the behavior of mice has recorded the time (in seconds) taken by each mouse to locate its food by considering 13 different mice as 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32. Find the median time that mice spent in searching its food.

**Solution :**

** 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32**

**Ascending order of given data is**

**27, 27, 28, 28, 29, 31, 32, 33, 33, 33, 34, 35, 63**

**Middle value is 7 ^{th} observation**

**Median = 32**

**Question 2 :**

The following are the marks scored by the students in the Summative Assessment exam

Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 |
Number of students 2 7 15 10 11 5 |
Cumulative frequency 2 9 24 34 45 50 (N) |

N/2 = 50/2 = 25^{th} value

Median class = 20 - 30

l = 20, N//2 = 25, m = 9, f = 15 and c = 10

Median = 20 + ([25 - 9]/15) x 10

= 20 + (16/15) x 10

= 20 + 1.06(10)

= 20 + 10.6

= 30.6

Hence the median of the given data is 31.

**Question 2 :**

The mean of five positive integers is twice their median. If four of the integers are 3, 4, 6, 9 and median is 6, then find the fifth integer.

**Solution :**

Let "x" be the fifth observation.

Mean of 5 observations = (3 + 4 + 6 + 9 + x)/5

= (22 + x)/5

Median = 6

Mean = 2 median

(22 + x)/5 = 2(6)

22 + x = 12(5)

22 + x = 60

x = 60 - 22

x = 38

Hence the 5th observation is 38.

After having gone through the stuff given above, we hope that the students would have understood, "Finding Median for Grouped Data"

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