Question

If the median of the distribution given below is 28.5, find the values of x and y.

Class interval	Frequency
0 - 10	5
10 - 20	x
20 - 30	20
30 - 40	15
40 - 50	y
50 - 60	5
Total	60

Answer 1

The cumulative frequency for the provided data is computed as follows.

Class interval	Frequency	Cumulative frequency
0 - 10	5	5
10 - 20	x	5 + x
20 - 30	20	25 + x
30 - 40	15	40 + x
40 - 50	y	40 + x +y
50 - 60	5	45 + x +y
Total	60

Observation from the table indicates that n = 60 

The equation 45 + x + y = 60 simplifies to x + y = 15 ……………………….(1)  
The median of the data is given as 28.5, which falls within the interval 20 − 30.  

Therefore, the median class is 20 − 30. 
The lower limit ( \(l\) ) of the median class is 20.  
The cumulative frequency ( \(cf\) ) of the class preceding the median class is 5 + x. 
The frequency ( \(f\) ) of the median class is 20.
The class size ( \(h\) ) is 10. 

The formula for the median is: Median = \(l + (\frac{\frac{n}2 - cf}{f})\times h\)

Substituting the values into the formula: 28.5 = \(20 + [\frac{\frac{60}2 - (5 +x)}{20}]\times 10\)

Simplifying the equation: 8.5 = \((\frac{25 - x}2)\)

Further simplification yields: 17 = 25 - x.
Solving for x, we get x = 8.

Using equation (1), substitute the value of x:  
8 + y = 15.
Solving for y, we get y = 7. 

Thus, the values of x and y are determined to be 8 and 7, respectively.