Question

What are the minimum, first quartile, median, mean, third quartile, and maximum of the following data set?: 10, 4, 9, 13, 5, 11, 5, 3, 7, 5

Answer 1

Minimum: 3

First quartile: 5

Median: 6

Third quartile: 10

Maximum: 13

Explanation:

First, let's list the data out from smallest to largest:
`3, 4, 5, 5, 5, 7, 9, 10, 11, 13`

The minimum is the lowest number in the data set.
Since we listed it out from smallest to largest, we know that the minimum is `3`.
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The median is the middle number. Cancel out `4` numbers from each side and we are left with `2` numbers:
`cancel(3), cancel(4), cancel(5), cancel(5), 5, 7, cancel(9), cancel(10), cancel(11), cancel(13)`

Find the average of the middle `2` numbers `5` and `7` to find the median:
`(5+7)/2 = 12/2 = 6`
Therefore, the median is `6`.
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The first quartile (Q1) is the median of the lower half of data which lies at 25% of the data.
Let's look at the lower half of numbers:
`3, 4, 5, 5, 5`

Cancel out `2` numbers from each side and we are left with the `Q1`:
`cancel(3), cancel(4), 5, cancel(5), cancel(5)`
Therefore, the `Q1` is `5`.
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The third quartile (Q3) is the median of the upper half of data which lies at 75% of the data.

Let's look at the upper half of numbers:
`7, 9, 10, 11, 13`

Again cancel out `2` numbers from each side:
`cancel(7), cancel(9), 10, cancel(11), cancel(13)`

The `Q3` is `10`.
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The maximum is the highest number in the data set; it is `13`.

Hope this helps!