Average shows the center point of the data.
Averages show what is in the center area of a dataset; hence measure central tendency. They are numbers that show the typical value, or the most representative number among all numbers. Different types of averages are calculated differently and give information about different things.
The two most frequently used methods to measure average are:
1. ARITHMETIC MEAN
2. MEDIAN
1. ARITHMETIC MEAN
What is arithmetic mean? It is the simple average – the sum of all items divided by the number of items in a dataset.
How to calculate arithmetic mean? Firstly, add value of all items to total all the results. Then, divide that number by the number of items in a dataset. The formula for arithmetic mean is:
Arithmetic mean = (x1 + x2 + (…) + xn) / n
Where:
x1 = Variable one, or item one
x2 = Variable two, or item two
(…)
n = Number of variables in the dataset
Uses of arithmetic mean in business management: It is used as an indicator of the average value when the range of results is small such as average sales levels, average inventory reorder levels, average workers’ wages, etc. per period of time. Arithmetic mean helps to compare two or more different datasets.
Example 1: The table below shows the numbers of hours that survey respondents watched television this month and last month.
| Number of hours per week (in hours): | |
|---|---|
| This month: | 10, 15, 5, 8 |
| Last month: | 1, 5, 10, 15 |
The arithmetic mean of this month’s results is 9.5 hours (38 hours / 4). This means that the respondents spent 9.5 hours on average per week watching television this month. The arithmetic mean of last month’s results is 7.75 hours (31 hours / 4). This means that the respondents had spent 7.75 hours on average per week watching television last month. The mean number of hours per week of watching television increased from 7.75 hours to 9.5 hours, or by 22.5%.
Advantages of arithmetic mean: It is simple and easy to calculate and understand. Also, all of the data is included in calculations. Additionally, arithmetic mean can be used in many business situations to make comparisons helping managers to better understand the results collected as well as to analyze data further using other methods of statistical analysis.
Disadvantages of arithmetic mean: It can be affected by a single extreme result that can skew the mean by a large amount. Hence, the arithmetic mean result would increase or decrease substantially making the result less meaningful. In addition, average means are often not a whole number; hence it might be difficult to interpret the numbers unambiguously.
2. MEDIAN
What is median? It is the middle item in a range of ordered data in a dataset. In case there is an even number of items in a dataset, the median will be the midpoint between these two central items.
How to calculate median? The method of calculating median depends whether the number of items in the dataset is even or odd. Firstly, start with arranging the items in ascending order.
A. MEDIAN OF EVEN NUMBERS: When the number of items in a dataset is an even number (e.g. 4, 6, 8, etc.), the median item can be identified by calculating the arithmetic mean of the two middle numbers. The first middle value is at the position:
1st middle value = n / 2
And the second middle value is at the position:
2nd middle value = (n / 2) + 1
So:
Median (even) = (1st middle value + 2nd middle value) / 2
Where:
n = Number of variables in the dataset
Example 2: If the number of values is 8, then 8 divided by 2 gives the 4th item as the first middle item, and 8 divided by 2 plus 1 gives the 5th item as the second middle item. The median is the simple average of the two middle values: the 4th item + the 5th item divided by two.
B. MEDIAN OF ODD NUMBERS: When the number of items in a dataset is an odd number (e.g. 5, 7, 9, etc.), the median item may be identified by using the following formula. The median is the middle value which is at position:
Median (odd) = (n+1) / 2
Where:
n = Number of variables in the dataset
Example 3: If the number of values is 7, then 7 + 1 divided by 2 gives the 4th item as the median item.
Uses of median in business management: Median divides the ordered dataset into two equal parts. Businesses organize their products into 50% best-selling products, employees into 50% who earn more than another half of workforce or advertising campaigns into 50% the most effective to increase sales revenue.
Advantages of median: Unlike arithmetic mean median is not distorted by extremely high and low items in the dataset. Hence, it is more representative and realistic in showing the central point of the dataset.
Disadvantages of median: It ignores all other items than the middle number (for sets of data with odd number of items) and two central items (for sets of data with even number of items). While the median (odd) shows the accurate number, the median is only an approximate value when there is an even number of items in the dataset – the arithmetic mean of the two middle numbers. Therefore, it can only be used in statistical analysis as estimation.
This article showed in details how numerical data might be summarized using the statistical techniques for calculating average. While the arithmetic mean shows the average value of the data sample, the median shows the exact middle value.
You can find out more about statistical analysis of market research results here.
