Median Practice Questions

Median is a measure of central tendency that represents the middle value of a dataset when the values are arranged in ascending or descending order.

Example 1: Find the median of the given data set 60, 70, 10, 30, and 50

Solution:

Median of the data 60, 70, 10, 30, and 50 is,

Step 1: Order the given data in ascending order as:

10, 30, 50, 60, 70

Step 2: Check if n (number of terms of data set) is even or odd and find the median of the data with respective ‘n’ value.

Step 3: Here, n = 5 (odd)

Median = [(n + 1)/2]^th term
Median = [(5 + 1)/2]^th term = 3^rd term
= 50

Example 2: Find the median of the given data set 13, 47, 19, 25, 75, 66, and 50

Solution:

Median of the data 13, 47, 19, 25, 75, 66, and 50 is,

Step 1: Order the given data in ascending order as:

13, 19, 25, 47, 50, 66, 75

Step 2: Check if n (number of terms of data set) is even or odd and find the median of the data with respective ‘n’ value.

Step 3: Here, n = 7 (odd)

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

Median = [(7 + 1)/2]^th term = 4^th term

= 47

Example 3: Find the Median of the following data.

If the marks scored by the students in a class test out of 100 are,

Solution:

For finding the Median we have to build a table with cumulative frequency as,

Marks	0-20	20-40	40-60	60-80	80-100
Number of Students	5	7	9	4	5
Cumulative Frequency	0+5 = 5	5+7 = 12	12+9 = 21	21+4 = 25	25+5 = 30

n = ∑f_i = 5+7+9+4+5 = 30(even)
n/2 = 30/2 = 15

Median Class = 40-60

Now using the formula,
Median = l + [(n/2 – cf) / f]×h

Comparing with the given data we get,

• l = 40
• n = 30
• f = 9
• h = 10
• cf = 12

Median = 20 + [(15 - 12)/6]×10
= 40 - (3/9) x 20
= 40 +6.6667
= 46.6667

Thus, the median mark of the class test is 46.67.

Example 4: Find the median number of hours studied per week

The following table shows the distribution of the number of hours spent studying per week by a group of students:

Solution:

For finding the Median we have to build a table with cumulative frequency as,

Hours Studied (Per week)	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25
Frequency	8	15	25	12	10
Cumulative Frequency	0 + 8 = 8	8 + 15 = 23	23 + 25 = 48	48 + 12 = 60	60 + 10 = 70

n = ∑f_i = 8 + 15 + 25 + 12 + 10 = 70(even)

n/2 = 70/2 = 35

Median Class = 10 - 15

Now using the formula,

Median = l + [(n/2 – cf) / f]×h

Comparing with the given data we get,

• l = 10
• n = 70
• f = 25
• h = 5
• cf = 23

Median = 10 + [(35 - 23)/25]×5

= 10 - (12/15) x 5
= 10 - (0.48) x 5
= 10 + 2.4
= 12.4

Thus, the median number of hours per week is 12.4 hours.

Related Articles

• Statistics
• Measure of central tendency
• Mean, Median, and Mode