Problems for Chapter 1

The table below records the lengths of reign (in years) of some of the rulers of England and Great Britain.

William I 21 Richard I 10 Edward III 50 Edward IV 22 William II 13 John 17 Richard II 22 Edward V 0 Henry I 35 Henry III 56 Henry IV 13 Richard III 2 Stephen 19 Edward I 35 Henry V 9 Henry VII 24 Henry II 35 Edward II 20 Henry VI 39 Henry VIII 38

a. What is the mean of the data?

b. What is the median of the data?

c. What is the mode of the data?

d. Which is the better description of the center of this data and why?

e. What is the standard deviation of the data?

f. Determine the five number summary of the data.

g. Make a stem and leaf plot of the data.

h. Make a box plot of the data.

i. Make a histogram of the data.

A researcher wants to see if birds that build larger nests lay larger eggs. He selects two random samples of nests: one of small nests and the other of large nests. He weighs one egg from each nest. The data are summarized below. What can be said about the variability of each group?

Small Nests Large nests Sample size 60 159 Sample mean (g) 37.2 35.6 Sample variance 24.7 39.0

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PRINTABLE VERSIONQuiz 1

Question 1

True or False: The number of days it rained where you live last month is an example of discrete data.

a) True

b) False

Question 2

True or False: The standard deviation is the square of the variance.

a) True

b) False

Question 3

Which of the following is not affected by an extreme value in the data set?

a) mean

b) mode

c) standard deviation

d) range

Question 4

Which of the following is an example of a data set with 5 values for which the standard deviation is zero.

a) 2,2,2,2,2

b) -1,-1,0,1,1

c) 1,2,3,4,5

d) -5,-4,0,3,5

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Question 5

If the test scores of a class of 35 students have a mean of 75.3 and the test scores of another class of 26students have a mean of 65.6, then the mean of the combined group is

a) 71.166

b) 70.450

c) 68.950

d) 68.666

Question 6

Given the first type of plot indicated in each pair, which of the second plots could not always be generatedfrom it?

a) dot plot, histogram

b) dot plot, stem and leaf

c) stem and leaf, dot plot

d) box plot, stem and leaf

Question 7

A survey was conducted to gather ratings of the quality of service at local restaurants. Respondents rated ona scale of 0 (terrible) to 100 (excellent). The data are represented by the following stem plot.

The median response was

a) 51

b) 50

c) 51.5

d) 52

Question 8

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Calculate the mean, median, mode, range and standard deviation of the data: -8, -7, -7, 6, 8

a) mean = -1.6, median = 6, mode = -8, range = 17, standard deviation = 7.9

b) mean = 1.0, median = -8, mode = -7, range = 15, standard deviation = 7.8

c) mean = 1.0, median = -7, mode = -7, range = 16, standard deviation = 7.8

d) mean = -1.6, median = -7, mode = -7, range = 16, standard deviation = 7.9

e) None of the above

Question 9

Calculate the mean, median, mode, range and standard deviation of the data: -108, -50, -50, 28, 88

a) mean = -2.8, median = -50, mode = -50, range = 196, standard deviation = 76.5

b) mean = -18.4, median = 28, mode = -108, range = 197, standard deviation = 76.6

c) mean = -18.4, median = -50, mode = -50, range = 196, standard deviation = 76.6

d) mean = -2.8, median = -108, mode = -50, range = 195, standard deviation = 76.5

e) None of the above

Question 10

The boxplots shown below summarize two data sets, I and II. Based on the boxplots, which of the followingstatements about these two data sets CANNOT be justified?

a) The median of data set I is equal to the median of data set II.

b) The range of data set I is greater than the range of data set II.

c) Data set I and data set II have the same number of data points.

d) The interquartile range of data set I is equal to the interquartile range of data set II.

Question 11

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The distribution that has the box plot shown could be described as

a) skewed left

b) skewed right

c) symmetrical

d) inconclusive

Question 12

The figure below shows a cumulative relative frequency plot of 40 scores on a test given in a Statistics class.Which of the following conclusions can be made from the graph?

a) There is greater variability in the lower 20 test scores than in the higher 20 test scores.

b) Sixty percent of the students had a test score above 80.

c) The median test score is less than 70.

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d) The horizontal nature of the graph for test scores of 60 and below indicates that those scores occurredmost frequently.

Question 13

The weights of male and female students in a class are summarized in the following boxplots:

Which of the following is NOT correct?

a) The median weight of the male students is about 166 lbs.

b) About 50% of the male students have weights between 150 and 185 lbs.

c) The mean weight of the female students is about 120 because of symmetry.

d) About 75% of the female students have weights more than 128 lbs.

Question 14

Given a data set consisting of 33 unique whole number observations, its five-number summary is:

What is the IQR?

a) 29

b) 30

c) 58

d) 59