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Mathematics

Calculate the mean and the median of the numbers:

2, 3, 4, 3, 0, 5, 1, 1, 3, 2.

Statistics

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Answer

By formula,

Mean =Sum of numbersNo. of numbers\text{Mean } = \dfrac{\text{Sum of numbers}}{\text{No. of numbers}}

Sum of numbers = 0 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 4 + 5 = 24

Mean =2410=2.4\therefore \text{Mean } = \dfrac{24}{10} \\[1em] = 2.4

Given,

Numbers : 2, 3, 4, 3, 0, 5, 1, 1, 3, 2.

First arrange the numbers in ascending order :

0, 1, 1, 2, 2, 3, 3, 3, 4, 5

Here, n = 10 which is even.

By formula,

Median=n2 th observation+(n2+1) th observation2=102 th observation+(102+1) th observation2=5 th observation+6 th observation2=2+32=52=2.5\text{Median} = \dfrac{\dfrac{n}{2}\text{ th observation} + \Big(\dfrac{n}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{10}{2}\text{ th observation} + \Big(\dfrac{10}{2} + 1\Big)\text{ th observation}}{2} \\[1em] = \dfrac{5 \text{ th observation} + 6\text{ th observation}}{2} \\[1em] = \dfrac{2 + 3}{2} \\[1em] = \dfrac{5}{2} \\[1em] = 2.5

Hence, mean = 2.4 and median = 2.5

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