Measures of Central Tendency

The data is about the hourly compensation cost for production workers in selected countries. Find the mean and modal class of the grouped data.

Write the steps to calculate the mean and modal class of the grouped data.

Step 1:

Calculate the class boundaries as the class limits must be continuous.

Subtract 0.005 units from the lower class limit to get the lower class boundary and add 0.005 units to the upper class limit to get the upper class boundary.

The class boundaries are:

Step 2:

Draw a table with class boundaries, frequency and the mid points of the data.

Step 3:

Calculate the last column by multiplying mid-points and frequency.

Step 4:

Calculate the mean with the formula.

Here, is the frequency of the class, is the mid-point of the class and is the total of frequency column from the above table.

Write the steps to find the modal class.

Step 1:

Draw a table of class boundaries with corresponding frequencies as shown in above table.

Step 2:

Find the class with highest frequency from the table. That class is called the modal class and the mode is the mid-point of that modal class.

Calculate the mean and modal class of the data.

(a)

Find the mean.

Here, is the value of.

Therefore, the mean of the data is:

Hence, the mean of the data is.

(b)

Find the modal class of the data.

Find the class with highest frequency from the above table. Since, 7 is the highest frequency but it has occurred twice in the table. Thus, consider both the classes as modal class. The first modal class is 2.475-7.485 and second modal class is 17.505-22.515.

Hence, the modal class areand.

The mean of the grouped data is $17.68 and the U.S. mean is $21.97. Hence, the mean of the hourly compensation cost for workers is less than the U.S mean.