Question

A random sample of employees from a local manufacturing plant pledged the following donations, in dollars, to the United Fund: 100, 40, 75, 15, 20, 100, 75, 50, 30, 10, 55, 75, 25, 50, 90, 80, 15, 25, 45, and 100. Calculate

(a) the mean;
(b) the mode.

Answer 1

The mean of the donated amounts is $50.50, and the modes are $75 and $100. The mean is obtained by dividing the sum of all donations by the total count and the mode(s) represent the most frequently occurring donation amounts.

Step-by-step explanation:

To calculate the mean donation, you sum all the donations and divide by the number of donations. For the given data set, the sum is $100 + $40 + $75 + $15 + $20 + $100 + $75 + $50 + $30 + $10 + $55 + $75 + $25 + $50 + $90 + $80 + $15 + $25 + $45 + $100 = $1,010. There are 20 donations, so the mean is $1,010 / 20 = $50.50.

To find the mode, which is the most frequently occurring value in the data set, we see that $75 and $100 both appear three times, more than any other amounts, making them the modes.

The explanation involves using basic statistical measures to summarize the data. The total sum for the mean is found by adding all given amounts, and the frequency of each value is determined to find the mode. These calculations help understand the central tendency and frequency distribution of the donations.