Question

the five number summary of a dataset was found to be: 45, 51, 57, 65, 69 an observation is considered an outlier if it is below: an observation is considered an outlier if it is above:

Answer 1

"an observation is considered an outlier if it is below: 30, an observation is considered an outlier if it is above 86"

Explanation:

Five Number Summary:

The five number summary of a dataset is composed of the following: minimum, quartile one, median, quartile three, maximum.

The minimum of a data set is simply the smallest value.

The quartile one is kind of like the median, or middle of the lower half of the data set, the 25th percentile.

The median is the middle of the data set, the 50th percentile.

The quartile three, similar to quartile one, is kind of like the median, or middle of the upper half of the data set, the 75th percentile.

Lastly the maximum of a data set, is simply the maximum value of a data set, or the biggest value.

Identifying Outliers:

Broadly speaking, outliers are simply values that are abnormally far from the values in the data set, hence the name outliers. The issue is what we define as being "far" from the values in the data set, but luckily we have an equation for this! We have two equations, one for high outliers and low outliers. A value is an outlier if one of the two is true:

`\text{outlier} < Q_1-1.5(\text{IQR})\\\text{outlier} > Q_3+1.5(\text{IQR})`

The
`Q_1\text{ and }Q_3` just represent the quartile one and three. The IQR part represents the Interquartile Range, which is just the difference of quartile 3 and 1, so:
`\text{IQR} = Q_3-Q_1`.

Now looking at the values given: 45, 51, 57, 65, 69 the 51 and 65 are the quartile one and three, so the IQR is:
`65 - 51 = 14` So plugging these values into the equations we get:

`\text{outlier} < 51-1.5(14)\\\text{outlier} > 65+1.5(14)`

Simplifying each inequalityy we get:

`\text{outlier} < 30\\\text{outlier} > 86`

So "an observation is considered an outlier if it is below: 30, an observation is considered an outlier if it is above 86"