Maths-

General

Easy

Question

# The median of the following data is

- 134.5
- 144.5
- 154.5
- 140.5

Hint:

**Median for grouped data :**

## The correct answer is: 144.5

### Given :

Steps to find median

Step 1 : Fix the class interval by subtracting 0.5 from lower limit and adding 0.5 to the upper limit of each interval

Class Interval
Frequency
109.5 - 119.5
5
119.5 - 129.5
25
129.5 - 139.5
40
139.5 - 149.5
60
149.5 - 159.5
40
159.5 - 169.5
25
169.5 - 179.5
5
n = 200

Step 2: Find the total number of observations(n) = 200

Step 3: Define the class size(h), and divide the data into different classes = 10

Step 4: Calculate the cumulative frequency of each class.

Class Interval
Frequency
Cumulative Frequency
109.5 - 119.5
5
5
119.5 - 129.5
25
30
129.5 - 139.5
40
70
139.5 - 149.5
60
130
149.5 - 159.5
40
170
159.5 - 169.5
25
195
169.5 - 179.5
5
200
n = 200

Step 5: Identify the class in which the median falls. (Median Class is the class where n/2 lies.)

Median class =

Thus the median class is 139.5 - 149.5

Step 6: Find the

lower limit of the median class(l) = 139.5,

and the cumulative frequency of the class preceding the median class (c) = 70

Now, use the following formula to find the median value.

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