Question

the table shows the weekly income of 20 randomly selected full - time students. if the student did not work, a zero was entered. (a) check the data set for outliers. (b) draw a histogram of the data. (c) provide an explanation for any outliers. (a) list all the outliers in the given data set. select the correct choice below and fill in any answer boxes in your choice. a. the outlier(s) is/are (use a comma to separate answers as needed.) b. there are no outliers.

Explanation:

Step1: Order the data

First, order the data set: 0, 0, 0, 0, 55, 106, 117, 141, 200, 207, 351, 409, 416, 471, 495, 505, 509, 514, 3074, 671.

Step2: Calculate quartiles

Find the median (Q2). Since there are 20 data - points, the median is the average of the 10th and 11th ordered values. Q2=$\frac{207 + 351}{2}=279$.
The lower half of the data is 0, 0, 0, 0, 55, 106, 117, 141, 200, 207. The median of the lower half (Q1) is the average of the 5th and 6th ordered values. Q1=$\frac{55 + 106}{2}=80.5$.
The upper half of the data is 351, 409, 416, 471, 495, 505, 509, 514, 3074, 671. The median of the upper half (Q3) is the average of the 5th and 6th ordered values. Q3=$\frac{495+505}{2}=500$.

Step3: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1 = 500 - 80.5 = 419.5.

Step4: Determine the outlier boundaries

The lower boundary for outliers is Q1−1.5×IQR = 80.5−1.5×419.5=80.5 - 629.25=- 548.75.
The upper boundary for outliers is Q3 + 1.5×IQR = 500+1.5×419.5=500 + 629.25 = 1129.25.

Step5: Identify outliers

Any data - point less than the lower boundary or greater than the upper boundary is an outlier. The values 3074 and 671 are greater than 1129.25.

Answer:

A. The outlier(s) is/are 671, 3074