Question

0. 0. 0. 0. 0. 1. 1. 1. 2. 2.   2.     2.     2.      2.       3.      3.      3.       3.       3.      8

A.) 5 NUMBER SUMMARY –

B.) BOX AND WHISKERS PLOT –

C.) OUTLIERS-

Answer 1

The first task is to compute the median and the quartiles. And, in order to compute the median and the quartiles, the data needs to be put into ascending order, as shown in the table below

Position	X (Asc. Order)
1	0
2	0
3	0
4	0
5	0
6	1
7	1
8	1
9	2
10	2
11	2
12	2
13	2
14	2
15	3
16	3
17	3
18	3
19	3
20	8

A)

Min = 0

Max = 8

Since the sample size n = 20 is even, we have that (n+1)/2 = (20+1)/2 = 10.5 is not an integer value, the median is computing by taking the average of the values at the positions 10th and 11th, as shown below

median =

Quartiles

The quartiles are computed using the table with the data in ascending order

For Q1​ we have to compute the following position:

Since 5.25 is not an integer number, Q1​ is computed by interpolating between the values located in the 5th and 6th positions, as shown in the formula below

For Q3​ we have to compute the following position:

Since 15.75 is not an integer number, Q3​ is computed by interpolating between the values located in the 15th and }16th positions, as shown in the formula below

B)

The interquartile range is therefore

Now, we can compute the lower and upper limits for outliers:

and then, an outcome X is an outlier if X < -3.875, or if X > 7.125

In this case, there is one outlier in the sample, and the outlier is 8. The following boxplot is obtained