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In Maths, Median is the middle value in the list of numbers.

Calculation:

To find the median, you will first need to arrange the given numbers in ascending order and then pick the middle number.

In the set { 12, 12, 13, 14, 15 }, there are 5 numbers in the list so the median is the middle number that is 13.

If there are an even number of numbers, then the median is the average of the middle two values.

Quartiles

Once we have found the position of the median, we can now find the position of the lower quartile and the upper quartile.

Position of the lower quartile is given by the formula ( n+1 ) /  4
Position of the upper quartile is given by the formula 3 ( n + 1) / 4
where n is the count of numbers in the given list.

The interquartile range is obtained using the formula = upper quartile - lower quartile

Related terms:

Mode: Mode is the value that occurs most often in the given set of numbers. So in the set { 12, 12, 13, 14, 15 }, the mode is 12. In case the set does not have any repetitive number, then there is no mode in the set.

Range: The range of a set of numbers is the difference between its largest number and the smallest number.
In the set { 12, 12, 13, 14, 15 }, the largest number is 15 and the smallest number is 12, so the range is calculated as 15 - 12 = 3

Mean: Mean is used to find a central value for a range of numbers. It is a type of average. For a given set of numbers, Mean is the total of the number divided by the count of the numbers in the set.
To find the mean of a given list of numbers { 2, 3, 7, 8, 10 }
First find the sum of the numbers = 2 + 3 + 7 + 8 + 10 = 30
Next find the total number of number = 5
Mean = Sum/ Count = 30 / 5 = 6

Practice questions:

Question: Determine the median, upper quartile, lower quartile and the interquartile range of the following numbers
5, 7, 4, 4, 6, 2, 8
First arrange the numbers in ascending order
2, 4, 4, 5, 6, 7, 8
Total count of numbers = 7
Hence median position = 7/2 = 3.5
Median = 5

Lower quartile position = 8 / 4 = 2
Lower quartile = 4

Upper quartile position = ( 3 * 8 ) / 4 = 6
Upper quartile = 7

Interquartile range     = upper quartile - lower quartile
= 7 - 4 = 3

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