Download Take-Home Quiz 6AB

6AB, MATH 1332, Fall 2012
Name___________________________________
Take-Home Quiz 6AB
Instructions: You may work with other students and get
outside help to answer the following questions.
However, you must show all of your work.
Find the median for the given sample data.
1) The number of vehicles passing through a bank drive-up line during each 15-minute
period was recorded. The results are shown below.
24 26 24 27 27 24 29 26 34 30 30 28 23 30 24 19 14 26 26 26
a) Find the mean number of vehicles going through the line in a fifteen-minute period.
Answer: Mean = 25.85
b) Find the median number of vehicles going through the line in a fifteen-minute period.
Answer: Median = 26
c) Find the mode of the number of vehicles going through the line in a fifteen-minute
period.
Answer: Mode = 26
Answer the question.
2) Tell which of the following distributions would have the least variation.
A) Weights of all pet dogs
B) Weights of all pet cats CORRECT ANSWER
C) Weights of all pets
D) Weights of all children who have a pet cat
b) Sketch a graph for a bimodal
distribution.
Frequency
Frequency
Sketch an appropriate graph.
3) a) Sketch a graph for a unimodal
right-skewed distribution.
Circle the appropriate response.
4) Of the mean, median, and mode, which is (are) affected by outliers?
A) The mean only CORRECT ANSWER
B) The median and mode
C) The mean and median
D) The mean and mode
5) A data set consists of 9 values which are not all the same (at least one is different). Which
of the following is possible?
A) The mode is equal to the largest value.
B) The mean is equal to the largest value.
C) The median is equal to the largest value.
D) None of the above is possible.
BOTH A AND C ARE CORRECT.
To make more sense, the question should read "Which of the following is NOT possible."
The answer would then be B.
Answer the questions.
6) The test scores of 15 students are listed below.
15 44 49 53 57 63 66 70 72 80 85 87 90 94 95
a) What is the mean test score?
Answer: Mean = 68
b) What is the median test score?
Answer: Median = 70
c) What is the mode?
Answer: No mode
d) What is the range? (Hint: the range is a single number)
Answer: Range = 95 - 15 = 80
e) Find the five-number summary for the data.
Answer:
Low: 15
Lower Quartile: 53
Median or Middle Quartile: 70
Upper Quartile: 87
High: 95
f) Draw a box-plot for this grade distribution in the space above the labeled axis below.
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
g) Explain what is meant by an outlier. Identify any outliers for this distribution.
Answer: An outlier is a data value that is much higher or much lower than almost
all of the other values in the distribution. An outlier for this dstribution is 15.
Find the standard deviation for the given data. Round your answer to the nearest penny, if
necessary.
7) The numbers listed below represent the amount of money that Tom has saved in each of
the last 8 months.
$142 $306 $144 $128 $347 $181 $401 $159
Compute the standard deviation.
Answer: 107.94
TO CALCULATE THE STANDARD DEVIATION OF A DATA SET
Step 1: Compute the mean of the data set.
Step 2: Subtract the mean from each data value. This gives the deviation from
the mean for each data value.
Deviation from the mean = data value — mean
Step 2: Square each of the deviations from the mean.
(Deviation from the mean)2
Step 3: Add all the squares of the deviations from the mean.
Step 4: Divide this sum by the total number of data values minus 1.
Sum of squares of deviations from the mean
Number of data values - 1
Step 5: Find the square root
deviation.
of this quotient. This number is the standard