Question

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of "each and every payroll voucher issued since January 1, 1993." Each payroll voucher was inspected and the following frequency distribution was compiled. Errors per Voucher Number of Vouchers 0-under 2 500 2-under 4 400 4-under 6 300 6-under 8 200 8-under 10 100 The mean number of errors per voucher is __________.

Answer 1

Answer:

3.67

Step-by-step explanation:

We are given the frequency distribution and we have to find the mean number of errors per voucher using the distribution.

The frequency distribution in correct format has been attached in the image below. The first two columns of the table represent the data given in the question.

For a frequency distribution(Grouped Data) the formula to calculate the mean is:

$Mean=\frac{\sum (xf)}{\sum (f)}$

Here x represents the midpoint of each class. Midpoint is the average of the lower class limit and the upper class limit. The midpoint of each class/group is calculated in the image below.

The midpoint of each class is then multiplied to the frequency of that class, which gives us "xf", the product of frequency and midpoints. This product for all classes is them summed up and divided by the sum of frequencies i.e. total frequency to get the mean for the grouped data.

From the table attached below:

$\sum (xf) = 500+1200+1500+1400+900=5500\\\\ \sum(f)=500+400+300+200+100=1500$

Therefore, the mean value will be:

$Mean=\frac{5500}{1500}=3.67$

Thus, rounded to 2 decimal places, the mean number of errors per voucher is 3.67