# probability and measures of variations.

Question 1

The two boxplots show the weights of the male and female students in a class.

Which of the following is NOT correct?

a. About 50% of the male students have weights between 150 and 183 lbs.

b. About 25% of female students have weights more than 128 lbs.

c. The median weight of male students is about 162 lbs.

d. The mean weight of female students is about 112.

e. The male students have more variability than the female students.

Question 2

A set of scores from a vocabulary test given to a large group of international students can be summarized with this five number summary: {20, 35, 45, 50, 60} Determine which of the following statements about the distribution CANNOT be

justified:

a. About 75% of the scores are equal to or above 35.

b. There are more scores from 35 to 45 than scores from 45 to 50.

c. The interquartile range is 15.

d. The distribution is skewed to the left or low end.

e. The range is 40

Question 3

Two sections took the same vocabulary quiz. Use the 5-number summary {20,30,35,45,60} to construct a boxplot for

Section I and use the summary {20,35,45,50,60} to construct a boxplot for Section II. Use the same scales for both plots,

of course. Based on the two boxplots, which of the following statements about the two sections CANNOT be justifies?

a. The median of Section II is greater than the median for Section I.

b. About 75% of the scores in Section II are greater than the or equal to about 50% of the scores in Section I.

c. There are the same number of scores in Section I and Section II.

d. The range of scores for Section I is equal to the range of scores for Section II.

e. The interquartile ranges are equal for both sections.

Question 4

Sam determined how much students spend per week on reading materials. He constructed separate graphs for those

who live on campus and those who live off campus.

Sam concluded that students who live off campus have different spending habits from those who live on cam pus.

a. Agree. Students who live off campus probably work and have more spending money.

b. Disagree. The medians are nearly equal.

c. Agree. There is more variability in costs for off-campus students than for on-campus students.

d. Disagree. The ranges are the same.

Question 5

Suppose that you measure the height of college woman and calculate a mean of 66 inches with standard deviation of

2.5 inches. Then you notice that the end of the measuring tape is badly worn and each woman’s height is one inch too

high. If you revise the measures by subtracting one inch from each value, determine the new mean and standard

deviation.

a. 66 inches and 2.5 inches.

d. 67 inches and 3.5 inches.

b. 66 inches and 1.5 inches.

e. 65 inches and 1.5 inch

c. 65 inches and 2.5 inches.

Question 6

In a study of heights of koala bears, scientists found that the distribution was strongly skewed left. However, in a study of

heights of polar bears, scientists found that the distrib ution was symmetric.

What measure of centre should the scientists use to describe their data?

a. Nothing. Bears are scary.

b. The koalas should be described with the median and interquartile range, and the polar bears with the mean and standard

deviation.

c. The koalas should be described with the mean and standard deviation, and the polar bears with the median and

interquartile range.

Question 7

Given the following data set: 3 5 6 7 7 8 8 8 9 9 9 10 102

Researcher detected the technical error in the last observation and replaced 102 by 10.2. What happens to Interquartile

Range (IQR) and Standard Deviation (SD)?

a. Both IQR and SD will increase.

b. The absolute value of IQR will change but the absolute value of SD will stay the same.

c. SD will decrease and IQR will not change.

d. Both IQR and SD will decrease.

Question 8

Which of the following sets of data has the largest standard deviation?

Set A: 57, 60, 60, 60, 60, 60, 60, 63

Set B: 57, 58, 59, 60, 61, 62, 63, 64

a. There is no way to tell without using a calculator.

b. Set A

c. Set B

Question 9

Two researchers collected the information about student’s monthly spending on rental DVD in two different campuses.

Researcher A: sample size n =125, Mean = $30, Standard Deviation = $5

Researcher B: sample size n =165, Mean = $15, Standard Deviation = $5

Select the best answer.

a. The variation of the data is not comparable because the sample size is different.

b. The variation of the data for researchers A and B is not comparable because the first mean is twice as large.

c. We cannot compare the variation because in calculating the standard deviations one researcher could have divided by (n)

and the other by (n-1)

e. The variation of data is similar for researchers A and B.

Question 10

Suppose a population generally has a symmetrical distribution with one of the measurements on this curve falls more than 3

standard deviations above the mean. What would you call this value?

a. An error. All the values should lie within 3 standard deviations of the mean.

b. A value that has a 99.7% chance of occurring, because of the Empirical Rule.

c. An extreme outlier.

d. None of the given answers.

Question 11

Shrek lives on a swamp. The condition of his swamp is very important to him so he regularly checks the temperature. Over

the course of the year he records the temperatures of his swamp. The median is 70 degrees, the first and third quartiles are

60 and 80 degrees respectively. The min and max temperatures were 26 and 115 degrees respectively. Were some

temperatures outliers?

a. Yes. There is at least one outlier and it is below the median

b. There are outliers both above and below the median

c. There are no outliers

d. Yes there is at least one outlier and it is above the median.

Question 12

A group of Statistics students took a 25-item multiple-choice test. Each question had four answers, only one of which was

correct. The correct answer was given a score of “1” and the wrong answers were given a score of “0”. The mea n and

standard deviation were computed, and the standard deviation was 0.

What we know about this distribution? Select the best answer.

a. The test was so hard that everyone missed all of the questions

b. About half of the scores were above the mean

c. Everyone correctly answered the same number of items

d. A calculation error must have been made in determining the standard deviation

Question 13

The amount of television viewed by today’s youth is of primary concern to Parents Against Watching Television ( PAWT). 300

parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched

television. The distribution of the data showed a bell-curved shape with the mean of 16 hours and the standard deviation of

4 hours.

Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the

distribution.

a. between 8 and 24 hours per week

b. between 4 and 28 hours per week

c. between 12 and 20 hours per week

d. less than 12 and more than 20 hours per week

Question 14

Assuming that resting systolic blood pressure for healthy woman under the age of 35 has a mean of 120 and a standard

deviation of 9. Also assuming that the distribution of these woman’s systolic blood pressures is unimodal and symmetric.

According to the Empirical Rule, about 16% of healthy woman of this age

a. have resting systolic blood pressure below 102.

b. have resting systolic blood pressure above 129.

c. have resting systolic blood pressure between 102 and 111.

d. have resting systolic blood pressure above 138.

Question 15

A town’s average snowfall is 49 inches per year with a standard deviation of 5 inches. The distribution is symmetric and bell

shaped. What amount of snowfall would you expect to be unusual for this town?

a. 53 inches

b. 63 inches

c. 35 inches

d. none of the given answers