Question

The table shows the weekly income of 2020 randomly selected​ full-time students. If the student did not​ work, a zero was entered. 0 463 0 0 501 103 527 231 329 385 3383 197 517 165 248 0 572 412 258 93 ​(a) Check the data set for outliers. ​(b) Draw a histogram of the data. ​(c) Provide an explanation for any outliers.

1. ​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

2. Choose the correct histogram below.

​(c) Choose the possible​ reason(s) for any​ outlier(s) below. Select all that apply.

A. Data entry error

B. A student providing false information

C. A student with unusually high income

D.None of the above

E. There are no outliers.

Answer 1

Answer A:

Arranging the data in Ascending Order-

0 , 0 , 0 , 0, 93 , 103 , 105 , 197 , 231 , 248 , 258 , 329 , 385 , 412 , 463 , 501 , 517 , 527 , 572 , 3383

Number of observations is 20.

The formula for calculation of the median is (( n/2 + (n/2 + 1) ) th observations / 2 )

The median of these observations is ( ( 10th. + 11th. ) observations / 2 ) =( (248 + 258) / 2) = 253

Now, taking the median of the 1st half of the observation set, that is, of the following set-

0 , 0 , 0 , 0, 93 , 103 , 105 , 197 , 231 , 248

The first quartile (Q₁) is (( 5th + 6th ) observations /2) = (93 + 103) / 2 = 98

Now taking the median of the 2nd half of the observation set , that is , of the following set-

258 , 329 , 385 , 412 , 463 , 501 , 517 , 527 , 572 , 3383

The third quartile (Q3) is (( 5th + 6th ) observations /2) = (463 + 501)/2 = 482

The Interquartile Range (IQR) = Third quartile - first Quartile = 482 - 98 = 384

Now let t = 1.5 x IQR = 576

Subtracting this value t from first quartile (Q₁) , and adding this value t to the   third quartile (Q3) , we get ,

t + Q₃ = 576 + 482 = 1058

Q₁ - t = 98 - 576 = -478

Therefore , if all the values of the observation set lie in the interval [-478 , 1058]. Then there are no outliers. If not, then there are outliers present in the data set.

The outlier is 3383.

Answer B:

The frequency distribution of the following data set is-

Class Intervals	Frequency
0-250	10
250-500	5
500-750	4
750-1000	0
1000-1250	0
1250-1500	0
1500-1750	0
1750-2000	0
2000-2250	0
2250-2500	0
2500-2750	0
2750-3000	0
3000-3250	0
3250-3500	1
Total	20

The histogram to the data set is-

( where X-axis represents the Class Intervals and Y-axis represents the Frequency )

Answer C:

The three Options A , B , C, can be the reason behind the outlier.

It can be any one of the three options.