Question

(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 $6 and ¼ 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. What is the average price per gallon?

Answer 1

1. Evaluate possible and probable outliers.

Outlier  r is an observation that lies an abnormal distance from other values in a random sample. There are various ways to detect outliers in a datset . Most commonly used method usage median and InterQuartile Range.

Datapoints beyond Q1 - 1.5*IQR Q3 +1.5*IQR (termed as inner fence) is known as possible outlier

Observations beyond Q1 - 3*IQR Q3 +3*IQR (termed as outer fence)is known as probale  outlier

where Q1- 1st Quartile =25th percentile Q3 = 3rd Quartile =75th Percentile ,

IQR -InterQuartile Range = Q3-Q1

Median Q3, Q1 and IQR can be calculated using xl formula of median and percentile

results are given below

From the table it is seen that 17 falls beyond 13.5 hence its a possible outlier

There is no probable outlier no datapoint is beyond 19.5

Median	5
Q1	3.5
Q3	7.5
IQR	4
Q3 +1.5IQR	13.5
Q1 -1.5IQR	-2.5
Q3 +3IQR	19.5
Q1 -3IQR	-8.5

2. In this case overall average canbe found by wage * proportion labour as overall adds upto 1

i.e (5/12)*5 +(1/3)*6+(1/4)*7 = (25+24+21)/12 = 70/12 = 35/6 $

3. 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..

This tells that amt invested is multipled by 1.01,1.04 1.16 for 1st 2nd and 3rd year respectively . hence average interest factor

will be (1.01 *1.04*1.16)^1/3 = 1.068 which means overall growth is equivalent 1.068³ = 1.218 = 1.01*1.04*1.16 .

Hence Geometric mean is the appropriate

If we use arithmetic mean average will 1.07 , Hence overall amount after 3 years should be 1.07³ =1.225 which is wrong

4. A plane travelled 200 miles at 600 mph and 100 miles at 500mph. What was the
average speed for the entire journey?

Distance travelled 300 miles

Time spent : 1/3 Hr for 1st 200 miles 1/5 Hr for next 100 miles total 8/15 Hr  

Hence average speed = 300*15/8 mile/Hr = 4500/8 = 562.5 mph

5.A driver purchased $10 worth of gasoline at $0.90 per gallon and another $10 at
$1.10 per gallon. What is the average price per gallon?

Money spent =20 $

Gasoline purchased = (10/0.9 )+( 10/1.1) = 11.11 +9.09 = 20.20

So average price/gallon = 20/20.20= $0.99 per gallon