# mathematics

**Show all work when appropriate. You may type your answers onto the test, or complete it by hand and submit a scanned copy.**

1. Given the following boxplot where *m* is the median value, what statement could be made about the distribution of the data?

Explain your answer.

**2.** The Colorado State Legislature wants to estimate the length of time it takes a resident of Colorado to earn a bachelor’s degree from a state college or university. A random sample was taken of 265 recentin-state graduates.

a) Identify the variable.

b)Is the variable quantitative or qualitative?

c)What is the implied population?

3. For the information in parts (a) through (g) below, list the highest

level of measurement as ratio, interval, ordinal, or nominal, and

**explain your choice.**

A student advising file contains the following information:

**(a)** Name of student

** (b) **Student I.D. number

** (c) **Cumulative grade point average

** (d) **Dates of awards (scholarships, dean’s list, etc.)

** (e) **Declared major

** (f) **A number code representing class standing:

1 = freshman, 2 = sophomore, 3 = junior,

4 = senior, 5 = graduate student

** (g) **Entrance exam rating for competency in English:

excellent, satisfactory, unsatisfactory

4. **Exam Scores **For **108** randomly selected collegestudents, this exam score frequency distribution wasobtained.

Class
Limits |
Class
Boundaries |
frequency | _{*Frequency} |
_{*Frequency} |
|||

90–98 | 89.5 – 98.5 | 6 | 94 | 8836 | |||

99–107 | 98.5 – 107.5 | 22 | 103 | 10609 | |||

108–116 | 107.5-116.5 | 43 | 112 | 12544 | |||

117–125 | 116.5-125.5 | 28 | 121 | 14641 | |||

126–134 | 125.5-134.5 | 9 | 130 | 16900 | |||

Total |

**Find by using the correct formulas:**

**Be sure to show all work.**

a) Mean

b) Modal class

c) Variance

d) Standard deviation

e) Constructa histogram

f) Discuss the shape of the distribution

5 .**Stories in the World’s Tallest Buildings **Thenumber of stories in each of the world’s 30 tallestbuildings is listed below.

88 88 110 88 80 69 102 78 70 55

79 85 80 100 60 90 77 55 75 55

54 60 75 64 105 56 71 70 65 72

a) Construct a stem-and-leaf plot

b) Find the 5-number summary

c) Construct a box-and-whiskers-plot

d) Check for outliers

e) Discuss the shape of the distribution

- Here clearly the data is not symmetrical as the very large dosage is expected to have a really high amount of drug dosage thus the data is somewhat positively skewed. And we know that for skewed data the median is the best measure to describe the location. So here the median would be best measure of position.
- Top quartile means top 25% of the data. Here the total number of mice are 40 so top quartile consists of (40*25%) = 10 mice. Now 40% of them survived so (10*40%) = 4 mice survived.
- The percentile would give us what percent of the mice are in that category. So in this example it will pin point the information we are looking for.
- The quartile is somewhat similar to percentile. The percentile divides the whole group into 100 equal parts and the quartiles into 4 equal parts. So quartiles would give the 25 percentiles information.
- The standard score will give us the relative measures. It will give enough information to compare to different scores by standardizing them.