Question

Below are the masses (in kg) of jobseekers who reported at the Directorate of Employment Centre in the state. Mass (kg)

50-54
55-59
60-64
65-69
70-74
75-79
80-84
85-89
90-94
These are the number of jobseekers and each of the masses 10, 20, 23, 15, 11, 6, 5, 3, and 7 respectively.
Use an assumed mean of 67kg to calculate, correct to one decimal place the mean of the distribution.

Answer 1

Explanation:

To calculate the mean of the distribution, we can use the formula for the mean of a frequency distribution:

where is the assumed mean, is the frequency of each class, and is the deviation of the class midpoint from the assumed mean.

First, we need to find the midpoints of each class. These are 52, 57, 62, 67, 72, 77, 82, 87, and 92.

Next, we calculate the deviation of each midpoint from the assumed mean of 67. These are -15, -10, -5, 0, 5, 10, 15, 20, and 25.

Then, we multiply each deviation by its corresponding frequency to get . These are -150, -200, -115, 0, 55, 60, 75, 60, and 175.

Finally, we sum up all the frequencies and all the values, and substitute these into the formula for the mean.

x=66.6