Question

The number of visitors to the Historic Museum for 17 randomly selected hours is shown.

6	31	33	35	35	39	41	48	49	54
57	57	58	59	60	60	91

a. Identify the five-number summary and the interquartile range (IQR)?

b. Construct a boxplot for the data?

c. Comment on the shape of the distribution.

d. Determine if there are any outliers?

Lower Fence Value:  

Upper Fence Value:

Answer 1

The five-number summary includes five values, namely,

• The minimum – this is the smallest value in our data set.
• The first quartile – this number is denoted Q₁ and 25% of our data falls below the first quartile.
• The median – this is the midway point of the data. 50% of all data falls below the median.
• The third quartile – this number is denoted Q₃ and 75% of our data falls below the third quartile.
• The maximum – this is the largest value

25% 25% 25% 25% + + Min + Q. Max Median

a.

Minimum = 6

Q₁ = 35

Median = 49

Mean = 47.82

Q₃ = 58

Maximum = 91

IQR = Q₃ - Q₁ = 58 - 35 = 23

b.

20 40 60 80

c. The data is slightly left skewed.

d. Any point lying outside (lower fence, upper fence) is said to be an outlier.

Lower fence = Q₁ - 1.5 $\times$ IQR = 35 - 1.5 $\times$ 23 = 0.5

Lower fence = Q₃ + 1.5 $\times$ IQR = 58 + 1.5 $\times$ 23 = 92.5

So, from upper fence and lower fence and also from the boxplot it is seen that there is no outlier in the data.