Question

The annual incomes of the five vice presidents of LEG Industries are $120,000, $128,000, $123,000, $130,000, and $150,000. Consider this a population.

a. What is the range?

b. What is the arithmetic mean income?

c. What is the population variance?

d. What is the standard deviation?

e. The annual incomes of officers of SSS Industries were also studied, and the standard deviation

was $8,612. Which firm had the greatest dispersion among its vice presidents’ salaries?

Answer 1

Given the annual incomes of the five vice presidents of LEG Industries are $120,000, $128,000, $123,000, $130,000, and $150,000.

Question (a)

Range = Highest Annual income - lowes Annual Income

= 150000 - 120000

= 30000

So Range is $30,000

Question (b)

Arithmetic Mean = Sum of all the Annual Incomes / Number of Annual Incomes

= 651,000 / 5

= 130,200

So Arithmetic Mean is $130,200

Question (c)

Population Variance 2 = [ (Xi - )2 ] / N

=[ (120,000 - 130,200)2 + (128,000 - 130,200)2 + 123,000 - 130,200)2 + (130,000 - 130,200)2 +  (150,000 - 130,200)2 ] / 5

= [ (-10,200)2 + (-2,200)2​​​​​​​ + (-7,200)2 + (-200)2​​​​​​​ + (19,800)2​​​​​​​ ] / 5

= ( 104040000 + 4840000 + 51840000 + 40000 + 392040000 ) / 5

= 552800000 / 5

= 110,560,000

So Population Variance is $110,560,000

Question (d)

Standard Deviaion =

= 110560000

= 10514.75154

So Standard Deviation is $10,514.75154

Question (e)

The annual incomes of officers of SSS Industries were also studied, and the standard deviation was $8,612

Standard Deviation tells us how spread or disperstion of the data is. If the Standard deviation is high, then the spread or dispersion of the data is more or if the Standard deviation is low, then the spread or dispersion of the data is less

Here the Standard Deviation of LEG Industries is $10,514.75 is more than that of the Standard Deviation of SSSIndustries whose value is $8,612

So LEG Industries had the greatest dispersion among its vice presidents’ salaries