Question

(i) The research director of a large oil company conducted a study of the buying habits of consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be -0.30.
(ii) Rainbow Trout, Inc., feeds fingerling trout in special ponds and markets them when they attain a certain weight. A group of 9 trout (considered the population) were isolated in a pond and fed a special food mixture called Grow Em Fast. At the end of the experimental period, the weights of the trout were (in grams): 124, 125, 123, 120, 124, 127, 125, 126 and 121. Another special mixture, Fatso 1B, was used in another pond. The mean of the population was computed to be 126.9 grams and the standard deviation was 1.20 grams. When these data are analysed, we discover that the food resulting in a more uniform weight is Fatso 1B.
(iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the standard deviation of this distribution were computed, it would be measured in hours squared

Which of these are true/false?

Answer 1

Answers;

i).

Given data,

Arithmetic mean=  11.5 gallons = 43.5322357 litres We know 1 Gallon= 3.7854118 litres

  median = 11.95 litres

  standard deviation= 4.5 litres

Since Mean > median , Implies data is positively skewed. Thus, Pearson's coefficient of skewness should be positive but here it is given to be negative which is FALSE.

ii). Rainbow Trout, Inc.,

Given,

   when food mixture called Grow Em Fast. is given

Weights (xi) = 124, 125, 123, 120, 124, 127, 125, 126 and 121.

Then

S.D. = 2.260777

Now,

   when food mixture called Fasto 1B is given, then

A.M. (Weights)=   126.9 grams

S.D.(Weights)= 1.20 grams

By comparing Arithmetic Mean (A.M.) and Standard Deviation (S.D.) for both the food mixture we can conclude that

food mixture called Fasto 1B gives more uniform weights. Since S.D. for Fasto 1B is lower. Thus, the given statement ;i.e. 'When these data are analysed, we discover that the food resulting in a more uniform weight is Fatso 1B' is CORRECT.

iii).

A study has been made of the number of hours a light bulb will operate before it burns out. If the standard deviation of this distribution were computed, it would be measured in hours squared

This given statement is FALSE. Since we know that standard deviation is positive square root of te variance. Thus it could never be squre hours.