Question

Record no. of days of medical leave taken by 30 employees within a year is given below.
No. of days 0-10 10-20 20-30 30-40 40-50
No. of Employees 5 7 11 4 3
Find the mean number of days of medical leave taken by an employee in a year.
A) 29.67 days
B) 25.67 days
C) 22.67 days
D) 20.6 days

Answer 1

Hint: To find the mean number of days of medical leave, the first step is to determine the midpoint (also called a class mark) of each class interval. These midpoints should then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of employees will be the value of the mean number of days.

Complete step-by-step answer:
Given
No. of days 0-10 ,10-20 ,20-30 ,30-40 ,40-50.
No. of Employees 5 ,7 ,11 ,4 ,3.
We have to find the mean number of days of medical leave
$Mean = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {{x_i}} }}$
$\begin{array}{*{20}{c}}
  {class}&{{f_i}}&{{x_i}}&{{f_i}{x_i}} \\
  {0 - 10}&5&5&{25} \\
  {10 - 20}&7&{15}&{105} \\
  {20 - 30}&{11}&{25}&{275} \\
  {30 - 40}&4&{35}&{140} \\
  {40 - 50}&3&{45}&{135}
\end{array}$
Where ${x_i}$ is the class mark (midpoint of class interval) and ${f_i}$ is the frequency and ${f_i}{x_i}$ is the product of class mark and frequency.
Sum of the frequencies is 30.
Sum of the ${f_i}{x_i}$ is 680.
$
  mean = \dfrac{{\sum {{f_i}{x_i}} }}{{\sum {{x_i}} }} \\
  mean = \dfrac{{680}}{{30}} \\s
  mean = 22.67 \\
 $
The mean number of days of medical leave taken by an employee in a year is 22.67 days.
So, the correct answer is “Option C”.

Note: Mean of any element is the average of its values. An interval is a range of values for a statistic. In grouped data, we have to find the class mark manually to find the mean. We solved the above problem using a direct method. Other methods to find mean are Assumed mean method and Step Deviation method.