Question

The ages of the employees in Kathy’s office are: 54, 23, 42, 59, 61, 44, 44, 50, 39, 40, 37, 43, 51, 34, 41,

40, 35, 49, 55, 58, 36, 43.
a. What is the median age?
b. How old are the youngest and oldest employees?
c. What are the lower quartile, upper quartile, and interquartile range?
d. Sketch a box plot using the points you found.

Answer 1

• a) 43,; b) 23 and 61; c) 39, 51 and 12

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Arrange the data in the ascending order:

• 23, 34, 35, 36, 37, 39, 40, 40, 41, 42, 43, 43, 44, 44, 49, 50, 51, 54, 55, 58, 59, 61

The minimum is 23, the maximum is 61, the median is 43 as both the middle numbers are 43.

The lower quartile is the median of the lower half of the data:

• 23, 34, 35, 36, 37, 39, 40, 40, 41, 42, 43

• Q1 = 39

The upper quartile is the median of the upper half of the data:

• 43, 44, 44, 49, 50, 51, 54, 55, 58, 59, 61

• Q3 = 51

Interquartile range is the difference of upper and lower quartiles:

• IQR = Q3 - Q1 = 51 - 39 = 12

You can easily sketch a box plot by using the 5-number summary:

• 23 ⇒ 39 ⇒ 43 ⇒ 51 ⇒ 61