Math 114 Quantitative Reasoning
Sections 2, 6, and 23 :: Fall 2011 :: Test 1
Name ______
Please show all necessary work.
For problems 1 through 3, refer to the following data sets:
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17S-1 / 0.7 / 0.9 / 0.9 / 1.1 / 1.3 / 1.5 / 1.6 / 1.8 / 1.9 / 2 / 2.4 / 2.6 / 2.7 / 2.9 / 3.1 / 3.2 / 5.8
S-2 / 0.7 / 1.5 / 1.7 / 2.1 / 2.4 / 3.5 / 3.8 / 4.2 / 4.9 / 5.8
(the top row is just labels, they’re not actual data values)
1. Make a stemplot for each data set. (Try to keep your columns neat) (10 points)
S-1S-2
2. If you wanted to describe the center of these data sets, would it be better to use the mean or median? Why? (10 points)
S – 1 Mean Median (circle one) Why?
S – 2 Mean Median (circle one) Why?
3. Using all of the data from both sets, create a histogram with 5 bars. Clearly label your histogram.
(14 points)
Class / Count4. I measured how long it took my students to take their Final Exams last semester and summarized the data with these boxplots: (2 points each)
/ MAT 114MAT 238
Duration (in minutes)
Which class would have the larger standard deviation? ______
The middle 50% of my MAT 114 students took how long to finish their Final? ______
Half of my 114 students were done with their Final before anyone finished their 238 Final. True / False
Everyone who took longer than about 85 minutes to finish their 238 Final got an A or a B. What percentage of students got an A or B? ______
Would you consider the distribution for MAT 238 to be skewed right or skewed left? Right / Left
The mean of the MAT 114 times would be ______the median (fill in the blank with: greater than, less than, or about the same as).
5. The number of Cottonwood seedlings found at 30 different sites along a section of the Colorado River are given in the following stemplot.
4 / 8 / 95 / 2 / 4 / 4 / 7
6 / 1 / 3 / 7 / 7 / 9
7 / 0 / 0 / 2 / 3 / 3 / 6 / 9 / 9
8 / 3 / 5 / 7
9 / 6 / 8
10 / 3 / 5 / 8
11 / 2
12
13 / 8 / 9
State the five number summary for this data set. (4 points)
Now, make a boxplot for this data set, using the axis provided below. (4 points)
40 / 55 / 70 / 85 / 100 / 115 / 130 / 1456. Suppose my data set has 13 values in it. How many data values are larger than Q3? (4 points)
7. Calculate the standard deviation of the following data set. Please use the exact values, i.e. do not round.
(16 points)
1.8 / 2.2 / 2.4 / 2.4 / 3.4 / 3.4 / 4Data values / Subtract the mean / Square
If I added the data values 2.8, 2.8, 2.8, and 2.9 to the above data set, would you expect the new set to have a higher or lower standard deviation than the original set? Explain. (Do not calculate the new standard deviation, just answer based on what you know about what standard deviation measures.)
8. A university wishes to summarize certain information at the start of the academic year. Which type of graph discussed in class would be the most appropriate for the following: (4 points each)
a) To show the proportion of total student enrollment broken down by its six colleges. (Arts, Science, Business, Education, Social Science and Professional)
b) To track the research monies awarded to the 6 colleges over the past 5 years.
9. A contractor has the opportunity to purchase a lot of 5000 used bricks at an auction, some of which are cracked and therefore unusable. The contractor wants to estimate what percentage of the bricks are cracked, but can’t inspect all 5000, so he instead looks through the 140 bricks on top and finds 15 which are cracked.
Match each vocabulary word below with its value or description on the right: (2 points each)
___ population a) 15/5000
___ sample b) 140
___ parameter c) 15/140
___ statistic d) entire lot of bricks
___ sample size e) percentage of entire lot which are cracked
f) bricks which were inspected
g) range of values within which 95% of values fall
h) 15
i) 125
Which specific type of sampling bias does this method of choosing a sample demonstrate? Why might this method of choosing a sample generate a sample which is not representative of the overall population? (8 points)