Question

(4)(a)Evaluate the following set of data for possible and probable outliers. 5 8 2 9 5 3 7 4 2 7 4 10 4 3 17 (b) A firm pays 5/12 of its labor force an hourly wage of $5, 1/3 of the labor force a wage of Sand / a wage of $7. Determine the average wage paid by the firm. (C)For the same amount of capital invested in each of 3 years, an investor earned a rate of return of 1% during the first year, 4% during the second year and 16% during the third. Find the simple arithmetic mean and the geometric mean. Which do you think is a more appropriate in this case? Explain. (d) A plane travelled 200 miles at 600 mph and 100 miles at 500mph. What was the average speed for the entire journey? (e) A driver purchased $10 worth of gasoline at $0.90 per gallon and another $10 at $1.10 per gallon. Determine the average price per gallon.

Answer 1

a) Arranging the numbers in ascending order:

2 2 3 3 4 4 4 5 5 7 7 8 9 10 17

n= 15

Q1 = (n+1)/4 th term = 16/4 = 4th term = 3

Q3= 3(n+1)/4 th term = (3*16)/4 = 12 th term = 8

Q2= Q3 - Q1 = 5

1.5*Q2 -Q1 = 4.5

1.5*Q2 + Q3 =15.5

An outlier is that data point of the given sample or given observation or in a distribution which shall lie outside the overall pattern. A Commonly used rule that says that a data point will be considered as an outlier if it has more than 1.5 IQR below the first quartile or above the third quartile.

In our case, the outliers are - 2 2 3 3 4 4 4 17

b) Average wage = (5/12 * 5 + 1/3 * 6 + 1/4 * 7) / 3 = 1.944

c) Arithmetic mean = (1+4+16) /3 = 7

Geometric Mean = $\sqrt(1*4*16) = 8$

Arithmetic mean is more reltable here because the rate of return earned throughout the year is an average not geometric mean.

d) Average speed= Total distance travelled / Average time taken

= (200 + 100) / (200/600 + 100/500) = 300/ (1/3 + 1/5) = 562.5 mph