Question

The data set below shows the number of books checked out from a library during the first two weeks of the month: 98, 19, 14, 15, 18, 16, 20, 22, 12, 17, 13, 21, 18, 15 Which of the following statements is true based on the data set? There is one outlier, indicating very few books were rented out on that day. There are two outliers, indicating very few books were rented out on those two days. There is one outlier, indicating an abnormally large number of books were rented out on that day. There are two outliers, indicating an abnormally large number of books were rented out on those two days.

Answer 1

C) Ther is one outliner , indicating an abnormally large number of books were rented out on that day

Answer 2

Answer:

(C)

Step-by-step explanation:

The given data set is:

98, 19, 14, 15, 18, 16, 20, 22, 12, 17, 13, 21, 18, 15

Arranging the given data set in ascending order, we get

12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 98

Since, outlier is an observation point which is quite different from the rest of the given data set values, thus from the given data set, 98 is an outlier as it is quite different from rest of the given data values.

Now, let us consider the data set values without 98,

12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22

The mean is:

$M=\frac{12+13+14+15+15+16+17+18+18+19+20+21+22}{13}=16.92$

Also,  let us consider the data set values with 98,

12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22,98

The mean is:

$M=\frac{12+13+14+15+15+16+17+18+18+19+20+21+22+98}{14}=22.71$

Now, in case of mean 16.92, the data values are almost symmetric in left and right side of the mean 16.92 but in case of mean 22.71, the data values are not symmetric in left and right side of the mean 16.92.

Thus, 98 is an outlier.

Therefore, There is one outlier, indicating an abnormally large number of books were rented out on that day.

Hence, option (C) is correct.