Math OER
Week 5 Homework, Part A

Two hundred college students were surveyed to find out how much they spent on textbooks last term, rounded to the nearest $50.

Cost of Textbooks	Frequency
$50	8
$100	34
$150	56
$200	40
$250	34
$300	10
$350	18

Those students were also asked their ages. Only 150 of them answered that question.

Age	Frequency
15 to 18	2
19 to 22	48
23 to 26	35
27 to 30	23
31 to 34	18
35 to 39	10
39 and over	14

1. Considering only the plain numbers (ignoring the units/labels), which data set has a larger range?

the textbooks, with a range of 300
the textbooks, with a range of 48
we cannot say because we do not know both ranges
we cannot say because one data set is categorical
we cannot say because not everyone answered the second question

2. Which outcome has the highest frequency?

$150 $350 19 to 22 years old 23 to 26 years old

3. Which outcome has the highest relative frequency?

$150 $350 19 to 22 years old 23 to 26 years old

4. If these data sets were drawn as pie charts, how large would the biggest wedge be?

50 degrees 58 degrees 101 degrees 115 degrees

5. What is the mean cost of textbooks?

$150 $190 $200 $253

6. What is the median cost of textbooks?

$150 $190 $200 $253

7. Which value could be the standard deviation for the textbook prices?

$5 $78 $160 $200

A survey of seventy LCC students asked about exercise and whether they homeschooled kids in 2020.

How Much are you Exercising?	Homeschooling	Not Homeschooling	Total
Not at all	16	10	26
A little, but not enough	10	18	28
Yes, enough	2	14	16
Total	28	42	70

8. What percentage were homeschoolers?

23% 40% 57% 60%

9. What percentage were homeschoolers who were getting enough exercise?

3% 5% 7% 13%

10. What percentage of homeschoolers were getting enough exercise?

3% 5% 7% 13%

Stay alert! The wording of problems 8 through 10 is purposefully legitimate but confusing. We know that percentages are found by thinking "part divided by whole". Carefully consider what numbers are the part and the whole in each problem. Sometimes this is not directly stated but only implied by the problem's wording!

A survey of fifty LCC students asked about their majors and favorite hobby.

	Hiking	Music	Art
Nursing	9	2	6
English	4	8	2
Psychology	11	5	3
Total	24	15	11

Short Answer Questions:

A. Can you have a Pareto histogram? Either sketch an example or explain why it is impossible.

B. Can you ever have a negative range? Either give an example of a data set with a negative range or explain why it is impossible.

C. Can categorical data have a median? Either give an example of such a data set or explain why it is impossible.