In this article, we will learn how to find Mean in Statistics. We will also use some easy examples to show you the math. Before that let us have a look at what the Mean is.
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What is Mean in statistics?
Mean is the average value of a given set of numbers. These numbers either belong to a sample data set or a population. The symbol x̅ represents the mean for a sample data set. The population Mean of a distribution is denoted by μ.
There are many kinds of mean values used as statistical measures. We would be talking about the Arithmetic Mean while referring to ‘Mean.’
Is Mean the same as average?
Yes! As mentioned above, the mean is the same as the average. Average has other meanings in the English language, and so does Mean. However, as far as the subject of statistics is concerned, Mean and average are the same.
Average is a term more commonly used in everyday language. It is not uncommon to hear, ‘what is the average stock price?’ On the other hand, Mean is more often used in statistical terminology. Statisticians ask, ‘what is the Mean life expectancy of a particular nation?’
Mean as a measure of central tendency
Mean is one of the measures of the central tendency of a data set, and the other two popular ones are median and mode. Summary statistics and measures of central location are alternate names for measures of central tendency.
A measure of central tendency aims to describe a central position within the data set with a single number. The mean may not fall right in the middle of the data set. Still, it estimates the magnitude of the average of the data points in the sample or population.
Consequently, mean can lead us astray if there are outliers. These extreme values are far removed from a bulk of the data points and can skew the data in one direction.
Therefore, the most suitable measure of central tendency to describe the center point of the data set depends on the spread of the data points. In many cases, the median or mode represents the sample or population more accurately.
How to find Mean in Statistics?
Let us see how to calculate/find mean of a data set
As stated above, the mean is nothing but the average of a data set. To calculate the mean of a sample or a population in Statistics, we need to add all the values in the data set and divide by the total number of data points.
Mean = (sum of all the data points/total number of data points)
The data set can have ungrouped or grouped data points. Unlike ungrouped data, we don’t know the exact values of the data points in the sample or the population for grouped data. However, we know the frequency of the data points occurring in the groups or intervals.
Mean (for grouped data) = (f1 * x1 + f2 * x2 + …. + fn * xn)/(f1 + f2 + … +fn) where fi and xi represent the frequency and the midpoint of the class interval respectively.
Sample Problems on finding the Mean
Example 1
What is the mean of ungrouped sample data set containing 2, 6, 12, 15, and 20?
Sum of all the data points = 2 + 6 + 12 + 15 + 20 = 55
Total number of data points = 5
Mean = 55/5 = 11
Example 2
The time (in minutes) taken by employees of company ABC to finish their lunch is
20  24  25  26  13  33  31  21  8  21  21  11  34  17  11  21  14  15  17  18 
Frequency distribution table of the time taken by the employees to finish their lunch
Time taken (in minutes)  Frequency (f_{i})  Midpoint (x_{i})  f_{i} * x_{i} 
1 ≤ t < 10  1  7.5  7.5 
10 ≤ t < 15  4  12.5  50 
15 ≤ t < 20  4  17.5  70 
20 ≤ t < 25  6  22.5  145 
25 ≤ t < 30  2  27.5  55 
30 ≤ t < 35  3  32.5  97.5 
Total  20  425 
Mean = 425/20 = 21.25
How to find Mean from a histogram
A histogram represents frequency table data drawn as a bar chart. We can use the formulas for calculating the mean for ungrouped or grouped data depending on what the histogram represents.
How to find mean in Excel
We use the native ‘AVERAGE’ formula to find the mean in Excel. We select AVERAGE from the formula dropdown menu containing formulas or type AVERAGE in the formula bar. Then, we select the cells containing the data. For example, if we want to calculate the mean for column G, rows two through 25, the formula will be ‘AVERAGE(G2:G25).’
For long data sets, excel proves very useful to find the Mean in statistics.
Refer to the blog posts ‘How to find median‘ and ‘How to find mode‘ in Statistics to learn how to calculate median and mode.
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7 years of teaching and writing experience, B. Tech. in Computer Science, Masters in Statistics from ISI.
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