Calculation of Mean, Median and Mode of Ungrouped Data
Mean, median, and mode are three basic ways to look at the value of a set of numbers. You will start by learning about the mean.
The mean, often called the average, of a numerical set of data, is simply the sum of the data values divided by the number of values. This is also referred to as the arithmetic mean. The mean is the balance point of a distribution.
Mean = sum of the values/the number of values
For instance, take a look at the following example. Use the formula to calculate the mean number of hours that Stephen worked each month based on the example below.
Example
Stephen has been working on programming and updating a Web site for his company for the past 15 months. The following numbers represent the number of hours Stephen has worked on this Web site for each of the past 7 months:
24, 25, 31, 50, 53, 66, 78
What is the mean (average) number of hours that Stephen worked on this Web site each month?
Step 1: Add the numbers to determine the total number of hours he worked.
24 + 25 + 33 + 50 + 53 + 66 + 78 = 329
Step 2: Divide the total by the number of months.
329/7 = 47
The mean number of hours that Stephen worked each month was 47.
The calculations for the mean of a sample and the total population are done in the same way. However, the mean of a population is constant, while the mean of a sample varies from sample to sample.
Example
Mark operates Technology Titans, a Web site service that employs 8 people. Find the mean age of his workers if the ages of the employees are as follows:
55, 63, 34, 59, 29, 46, 51, 41
Step 1: Add the numbers to determine the total age of the workers.
55 + 63 + 34 + 59 + 29 + 46 + 51 + 41 = 378
Step 2: Divide the total by the number of months.
378/8 = 47.25
The mean age of all 8 employees is 47.25 years, or 47 years and 3 months.
Look at another approach. If you were to take a sample of 3 employees from the group of 8 and calculate the mean age for these 3 workers, would the results change?
Read more below-
SS1 Mathematics Third Term: Calculation of Mean, Median and Mode of Grouped Data
