Mean Median Mode Formula

The Mean, Median and Mode are the three measures of central tendency. Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set. The median is the middle number in a data set when the numbers are listed in either ascending or descending order. The mode is the value that occurs the most often in a data set and the range is the difference between the highest and lowest values in a data set.

The Mean

\[\large \overline{x}=\frac{\sum x}{N}\]

Here,
$\sum$ represents the summation
X represents observations
N represents the number of observations .

The Median

If the total number of observations (n) is an odd number, then the formula is given below:

\[\large Median=\left(\frac{n+1}{2}\right)^{th}observation\]

If the total number of the observations (n) is an even number, then the formula is given below:

\[\large Median=\frac{\left(\frac{n}{2}\right)^{th}observation+\left(\frac{n}{2}+1\right )^{th}observation}{2}\]

The Mode

\[\large The\;mode\;is\;the\;most\;frequently\;occuring\;observation\;or\;value.\]

Solved Examples

Question: Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

Solution:

Given data: 13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average.

Mean = $\frac{13+18+13+14+13+16+14+21+13}{9}=15$

(Note that the mean is not a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.)

The median is the middle value, so to rewrite the list in ascending order as given below:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be

$\frac{9+1}{2}=\frac{10}{2}=5$

= 5th number

Hence, the median is 14.

The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

Mean = 15
Median = 14
Mode = 13
Range = 8

8 Comments

  1. Very nice

  2. very nice app/website

  3. Very helpful…

  4. Define mean, median, mode and state formulas for each of them (grouped and ungrouped)? What is range?

  5. Thank you it was very helpful for me

  6. This cleared my doubt. THANKS:)

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