Question

Use the following data set to complete the questions below. Calculate the five number summary and sketch a box and whisker plot. Be sure to label your box plot correctly. 78 74 76 80 85 81 62 80 91 46 20 94 95 96 91 82 (a) Calculate the five number summary. (b) Calculate the interquartile range and determine any potential outliers. (c) Sketch a boxplot. Be sure to label your boxplot correctly. (d) Write one inference you can make about this data based on your work above.

Answer 1

For this question we first arrange the data in ascending order

	X
1	20
2	46
3	62
4	74
5	76
6	78
7	80
8	80
9	81
10	82
11	85
12	91
13	91
14	94
15	95
16	96

a)

For the five point summary we need min,Q1,Q2,Q3,max. Where the quartiles use the following formula

i(1+N) value 4

Quartile	th value	Value
Q1	4.25	74.5
Q2	8.5	80.5
Q3	12.75	91

five point summary
Min	20
Q1	74.5
Q2	80.5
Q3	91
Max	96

b)

IQR = Q3-Q1

IQR = 16.5

To check for outlier we see if any value falls outside the range (Q1-1.5IQR, Q3 - 1.5IQR)

Range: (49.75, 115.75)

X:outliers

20

46

Since they do not fall int the range they are outliers.

c)

Since now that we have outliers, we remove them from our summary and plot them separately

five point summary
Min	62
Q1 lower	74.5
Q2 median	80.5
Q3 upper	91
Max	96

We use these the min and max to make the endpoint of whisker. The side of the box is the lower quartile left side and upper quartile right side. The middle line is the median

62 745 803 5 96 + 十 十 - + 70 50 55 60 65 AC 85 90 95 TOO

the technology doesn't provide to plot the outliers, please plot them when manually making the graph.

d)

We can see that the median is towards the left and more space is on the right side of the box, so we assume that this is postively / right skewed data.