Question

a data set has its first and third quartiles as 9 and 17 respectively. Which of the following data points would be considered an outlier for the data set

A. 27

B. 17

C. 3

D. 41

In which of these cases should the mean be used?

A. When the data is left-skewed

B. When the data is symmetric

C. When the data is right-skewed

D. When the data has extreme values

Answer 1

a data set has its first and third quartiles as 9 and 17 respectively. Which of the following data points would be considered an outlier for the data set?

D. 41

Explanation:

We are given

Q1 = 9

Q3 = 17

IQR = Q3 – Q1 = 17 – 9 = 8

1.5*IQR = 1.5*8 = 12

Q1 - 1.5*IQR = 9 – 12 = -3

Q3 + 1.5*IQR = 17 + 12 = 29

So, numbers outside -3 and 29 are considered as outliers.

So, number 41 is outside this interval, therefore it is considered as an outlier.

In which of these cases should the mean be used?

B. When the data is symmetric

Explanation:

For the skewed data, the mean is not very effective. Also, if there are extreme values, then these values affect the value of the mean, so mean is not good in this condition. Mean is only better when data is symmetric.