Question

The following frequency distribution describes the ages of the employees at a clothing store.

Age	15-24	25-34	35-44	44-54	55-64
Frequency	13	4	3	2	2

a. What proportion of the employees is older than 24 years old?

b.Describe the shape (symmetric, uniform, skewed left, or skewed right) of the distribution.

c.For this distribution, which measure of center (mean or median) is most likely to be the largest?

Answer 1

Age	15-24	25-34	35-44	45-54	55-64	Total
Class Mark (x)	19.5	29.5	39.5	49.5	59.5
Frequency (f)	13	4	3	2	2	24
Probability	0.5417	0.1667	0.125	0.0833	0.0833	1

Let X be the age of the employees.

a) P( X > 24 ) = 0.1667 + 0.1250 + 0.0833 + 0.0833 = 0.4583

b) Since large amount of data points are concentrated towards the lower part, we conclude that the data is skewed towards the right i.e. the data is rightly skewed.

c) Mean =   = 708 / 24 = 29.5

And Median =   
where L is the lower limit
I is the interval of median class
n is the number of all observations
fm is the frequency of median class
and is the cumulative frequency from classes before the median class

Median = 15 + 9*(12 - 0)/13 = 23.3077 = 23.

Thus, Mean > Median.

Hope this answers your query!