Question

Nine industrial workers were tested for gripping strength and the mea-
surements were 128.3, 106.5, 93.9, 116.6, 152.4, 125.0, 132.1, 105.8,
136.7.
(a) Obtain the rst and third quartiles (Q1 and Q3), median, and IQR.
Interpret Q1 and Q3. What does IQR represent?

(b) Construct a ve-number summary box-plot for this data and com-
ment on the shape of the distribution of the data.

(c) Check to see whether the data contain any outliers.

Answer 1

Solution:-

a)

Median = 1/2(n+1)^th term

Median = 125.0

Minimum: 93.9
Quartile Q1: 106.15
Median: 125.0
Quartile Q3: 134.4
Maximum: 152.4

IQR = 3rd quartile - 1st quartile

IQR = 134.4 - 106.15

IQR = 28.25

Quartile 1 is the middle point of the minimum data point and the median.

Quartile 3 is the middle point of the maximum data point and the median.

IQR represents the middle 50% of the data points in the distribution.

b)

c) No, there are no outlier in the data set.