Problem 6E

The relative frequency histogram given next was constructed from data obtained from a random sample of 25 families. Each was asked the number of quarts of milk that had been purchased the previous week.

a Use this relative frequency histogram to determine the number of quarts of milk purchased by the largest proportion of the 25 families. The category associated with the largest relative frequency is called the modal category.

b What proportion of the 25 families purchased more than 2 quarts of milk?

c What proportion purchased more than 0 but fewer than 5 quarts?

Solution 6E

Step1 of 4:

Let us consider a relative frequency Histogram it presents number of quarts of milk that had been purchased the previous week:

Here our goal is:

a). We need to determine the number of quarts of milk purchased by the largest proportion of the 25 families by using this relative frequency histogram.

b). We need to find the proportion of the 25 families purchased more than 2 quarts of milk.

c). We need to find the proportion purchased more than 0 but fewer than 5 quarts.

Step2 of 4:

a).

From the above given Relative frequency Histogram we can say that more number of people falls under 2 quarts modal category. Therefore 9 out of 25 people falls in this category.

Step3 of 4:

b).

From the above given Relative frequency Histogram we can say that out of 25 families 9 people purchased more than 2 quarts of milk.

That is quarts 3 has relative frequency 0.2

quarts 4 has relative frequency 0.12

quarts 5 has relative frequency 0.04

Now,

Proportion = 0.2 + 0.12 + 0.04

= 0.36

Hence, Proportion is 36%.

Step4 of 4:

c).

From the above given Relative frequency Histogram we can say that out of 25 families 8% people purchased from 0 Quarts and 4% people purchased from 5 Quarts of milk.

That is quarts 1 has relative frequency 0.2

quarts 2 has relative frequency 0.36

quarts 3 has relative frequency 0.2

quarts 4 has relative frequency 0.12

Now,

Proportion = 0.2 + 0.36 + 0.2 + 0.12

= 0.88

Hence, Proportion is 88%.