Answer to Question #203675 in Statistics and Probability for pooja

Question

A research was conducted to improve the safety plans in a factory. In this study, the accidental data of the factory for the last 50 weeks were compiled. These data are grouped into the frequency distribution as shown below:

Number of Accidents

Numbers of Weeks

0-5

8

5-10

22

10-15

10

15-20

8

20-25

2

Draw a histogram and calculate the average number of accidents per week.

Answer 1

Solution:

We need to compute the sample mean for these provided grouped data:

Now, we need to construct the midpoints based on the lower and upper limits of all the classes provided:

Now, with the midpoints, we need to multiply each midpoint for its corresponding frequency, as shown in the table below:

$\begin{array}{ccl} \bar X & = & \displaystyle \frac{1}{N} \sum_{i=1}^k M_i \cdot f_i \\\\ \\\\ & = & \displaystyle \frac{1}{50}\left( 2.5 \cdot 8+7.5 \cdot 22+12.5 \cdot 10+17.5 \cdot 8+22.5 \cdot 2 \right) \\\\ \\\\ & = & \displaystyle \frac{495}{50} \\\\ \\\\ & = & 9.9 \end{array} ​$

Therefore, based on the data provided, the sample mean for these grouped data is $\bar X = 9.9$

Histogram