Question

Monthly Salaries

A sample of 100 graduates who completed a 6-month security guard training program reported the following monthly starting salaries (in security guard related employment).

Monthly Salary	Number of Graduates
$1,001-$1,400	1
$1,401-$1,800	11
$1,801-$2,200	14
$2,201-$2,600	38
$2,601-$3,000	36
Total	100

1. Compute the (approximate) mean monthly starting salary. [4 marks]
2. Compute the (approximate) standard deviation of the monthly starting salaries. [6 marks]
3. Hand-sketch a relative frequency histogram, using a percentage scale on the Y-axis. Do not be concerned with drawing the graph exactly to scale. Based on the sketch, determine if the distribution of the salaries is positively or negatively skewed. What does the skewness reveal, in terms of the distribution of starting salaries? [6 marks]

Answer 1

Let's calculate the mean and standard deviation. The calculations are shown in the below table:

x	f	x (Midpoint)	x^2	f.x	f.x^2
1001-1400	1	1200	1440000	1200	1440000
1401-1800	11	1600	2560000	17600	28160000
1801-2200	14	2000	4000000	28000	56000000
2201-2600	38	2400	5760000	91200	218880000
2601-3000	36	2800	7840000	100800	282240000
Total	100		21600000	238800	586720000

a) Mean = 238800/100 = 2388

b) Standard deviation is calculated by the formula:

Insert the values from the table above, we get: s = 407.89

c) The relative frequency histogram is: