Summarizing Data Numerically
Name _______________________________
Chapter 3 Homework
Read each problem carefully. Write your answer in the blank, or circle the correct answer.
1. An insurance company crashed a sample of six cars of the same model at 5 mph. The costs of repair
for each of the crashes were: $415, $426, $465, $310, $405, and $242.
Calculate the following using 1-VarStats. Round any decimal answers to 1 decimal.
Mean repair cost = __________
Median repair cost = __________
Range of repair costs = __________
Standard deviation of repair costs = ___________
2. For the histogram shown, determine if the mean is greater than, less than, or equal to the median.
a)
b)
c)
d)
e)
Mean = Median because the histogram is symmetric
Mean < Median because the histogram is skewed right
Mean < Median because the histogram is skewed left
Mean > Median because the histogram is skewed right
Mean > Median because the histogram is skewed left
3. The following histogram represents the connection time in seconds to an internet provider.
Which measure of central tendency best describes the “center”
of the distribution?
a) Mean because the distribution is skewed
b) Mean because the distribution is symmetric
c) Median because the distribution is skewed
d) Median because the distribution is symmetric
Which measure of distribution best describes the variation of the distribution?
a) Standard Deviation because the distribution is skewed
b) Standard Deviation because the distribution is symmetric
c) IQR because the distribution is skewed
d) IQR because the distribution is symmetric
4. Which of the following histograms depicts a higher standard deviation?
Histogram A
Histogram B
a) Histogram A depicts a higher standard deviation because the distribution has more
dispersion.
b) Histogram B depicts a higher standard deviation because the distribution has more
dispersion.
c) Histogram B depicts a higher standard deviation because its highest bar is higher than the
highest bar in A.
d) Histogram B depicts a higher standard deviation since it is more bell shaped.
5. The following data for a random sample of banks in two cities represents the ATM fees for using
another bank’s ATM.
City A
2.50
1.25 1.25
0
1.75
City B
1.5
1.00 1.50 1.50 1.00
Compute the sample standard deviation for ATM fees for each city. Round each to 2 decimals.
Standard deviation for City A: ___________
Standard deviation for City B: ___________
Which city has the most dispersion based on your answers to part (a)?
a) City A, because it has a lower standard deviation.
b) City B, because it has a lower standard deviation.
c) City A, because it has a higher standard deviation.
d) City B, because it has a higher standard deviation.
6. Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation
of 12. Use the Empirical Rule to determine the following:
What percentage of people have an IQ score between 76 and 124? _______________
What percentage of people have an IQ score less than 76 or greater than 124? ______________
What percentage of people have an IQ score greater than 136? ______________
7. Babies born after a gestation period of 34 weeks have a mean weight of 2600 grams and a standard
deviation of 700 grams. Babies born after a gestation period of 40 weeks have a mean weight of
3200 grams and a standard deviation of 465 grams. If a 34-week gestation period baby weighs 3025
grams and a 40-week gestation period baby weighs 3625 grams, calculate their z-scores (2 decimals).
32-week baby:
z-score = ___________
Is this above or below the mean? ___________
40-week baby:
z-score = ___________
Is this above or below the mean? ___________
Which baby weighs relatively more?
a) The baby born in week 34 since it’s z-score is smaller.
b) The baby born in week 40 since it’s z-score is smaller.
c) The baby born in week 34 since it’s z-score is larger.
d) The baby born in week 40 since it’s z-score is larger.
8. A highly selective boarding school will only admit students who place at least 2 standard deviations
above the mean on a standardized test that has a mean of 300 and a standard deviation of 24. What
is the minimum score than an applicant must make on the test to be accepted?
Minimum score = ______________
9. Explain the meaning of the statement “The 90th percentile of the length of newborn females in a
certain city is 53 cm”.
a) 90% of newborn females have a length of 53 cm or less, and 10% of newborn females have a
length that is more than 53 cm.
b) 90% of newborn females have a length of 53 cm or more, and 10% of newborn females have
a length that is less than 53 cm.
c) 90% of newborn females have a length of 53 cm.
10. The following data represents the inches of rainfall in April for a certain city over the course of 20
years.
0.56 2.15 3.62 5.18 1.03
2.62 3.89 5.32 1.25 2.98
4.17 5.46 1.61 3.39 4.61
5.89 1.97 3.51 4.75 5.99
Determine the quartiles:
(do not round!!!)
Q1 = __________
Q2 = __________
Q3 = __________
Calculate the IQR:
IQR = __________
Calculate the Lower Fence:
Lower Fence = ___________
Calculate the Upper Fence:
Upper Fence = ___________
Are there any outliers in the data set? (yes/no)
If there are outliers, list them: __________________________________
11. Identify the shape of the distribution and determine the 5-number summary.
What is the shape of the distribution?
a) Skewed Right
b) Skewed Left
c) Symmetric
The shape of the distribution is based on the ____________________________.
(Box, Whiskers)
The five-number summary is:
Min = ____________
Q1 = _____________
Q2 = _____________
Q3 = _____________
Max = ____________
(each number in the 5-number summary is a whole number)
12. Use the following box plots to answer the following questions.
Which variable has more dispersion? ________
Determining which variable has more dispersion is based on the ____________________________.
(Box, Whiskers)
What is the shape of variable X? _______________________
What is the shape of variable Y? _______________________
13. The following data represent the age of world leaders on their day of inauguration. Find the five
number summary, and construct a boxplot for the data.
50
48
55
The five-number summary is:
41
44
61
65
52
58
55
69
44
Min = ____________
Q1 = _____________
Q2 = _____________
Q3 = _____________
Max = ____________
Which of the following is the correct boxplot for the data?
a)
What is the shape of the distribution?
a) Roughly symmetric
b) Skewed Left
c) Skewed Right
b)
c)
62
48
56