Mean calculator
Find the mean of a discrete data set and know the different properties of the data using this calculator.
For instance, the mean calculator along with giving the mean with a step-by-step solution gives the total number of data, sorted array, and smallest and largest data values.
What is the mean of a data set?
One word to describe the mean is “average value”. A value that lies between both extremes of the data.
There are other types of means like harmonic and geometric but the basis of it all or the “Actual mean” is the arithmetic mean.
Mean formula:
Small X bar is the notation used for mean in mathematics although it is represented differently in statistics. N is the number of data set values. Sigma notation means summation.
How to calculate the mean?
Find the summation of the whole data. Count how many values are present in the data. Divide the summation by that number. The answer is the mean of the data.
Alternatively, use the mean calculator.
Example of Calculating the Mean for Ungrouped Data:
Find the mean of the following data set:
10, 10, 34, 23, 54, 9, 10, 2, 38, 23, 38, 23, 21
Solution:
Follow these steps to calculate the mean of Ungrouped data
Alternatively, you can use a mean calculator for Ungrouped data to streamline this process.
Step 1: Add the data.
= 2+9+10+10+10+21+23+23+23+34+38+38+54
= 295
Step 2: Count the values.
There are a total of 13 values.
Step 3: Divide the sum by 13.
= 295/13
= 22.692
The mean of the Ungrouped data is 22.692.
Example of Calculating the Mean for Grouped Data:
Consider the following data set which represents the marks obtained by students in a test. The marks are grouped into intervals:
Marks (Interval) | Frequency (f) |
0 - 10 | 3 |
10 - 20 | 5 |
20 - 30 | 8 |
30 - 40 | 4 |
40 - 50 | 2 |
Calculate the mean of the given data.
Solution
Follow these steps to calculate the mean of grouped data
Alternatively, you can use a mean calculator for grouped data to streamline this process.
Step 1: Calculate the Midpoints
Marks (Interval) | Frequency (f) | Midpoint (x) | f⋅x |
0 - 10 | 3 | 5 | 15 |
10 - 20 | 5 | 15 | 75 |
20 - 30 | 8 | 25 | 200 |
30 - 40 | 4 | 35 | 140 |
40 - 50 | 2 | 45 | 90 |
Step 2: Calculate the Sum of f⋅x
Σ(f⋅x) =15+75+200+140+90=520
Step 3: Calculate the Total Frequency
Σf = 3+5+8+4+2=22
Step 4: Calculate the Mean
Mean=Σ(f⋅x)/ Σf
=520 / 22
≈23.64
The mean of the grouped data is 23.64.