Question

The following dotplot shows the centuries during which the 11 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle.
According to the 1.5 ⋅ IQR rule for outliers, how many high outliers are there in the data set?

Answer 1

Taking into account the rule 1.5 IQR, there aren't high outliers in the displayed data set.

Calculation of the Interquartile Range and the rule 1.5 IQR.

To calculate the Interquartile Range IQR, you must subtract the value of the first quartile Q1, to the third quartile Q3, as you can see in the formula below:

IQR = Q3 - Q1

Using the five-number summary, you can replace the formula:

IQR = 17 - 13

IQR = 4

Before to apply the rule 1.5 IQR, you must multiply the IQR by 1.5:

4 * 1.5 = 6

Now, to apply the rule you must add the value obtained (6), to the third quartile (17), if any data is over this, theoretically it's an outlier:

17 + 6 = 23 (As you do not have any data over this value, it is identified that there are no outliers in the upper section).

Finally, you must subtract the value obtained (6) to the first quartile (13), if any data is under this, theoretically it's an outlier:

13 - 6 = 7 (Since you don't have any castle data built before this century, there wouldn't be any theoretically outliers either).

By this reason, using the rule of 1.5 IQR, you can see there aren't outliers in the displayed data set.

brainliest please if correct.