Chapter 3

Looking at the provided population data, calculate the population mean.

$35.8 billion

A data set has Q1 = 12 and Q3 = 20. Which measurements in the set { -2, 1, 30, 31} would be considered outliers?

-2

Calculate the z score for the population value 6.5 where μ = 7.96 and σ = 0.42 (rounded to two decimals).

-3.48

A data set has Q1 = 7 and Q3 = 11. Determine the lower and upper limits for a box plot.

1 and 17

Determine the variance of the following population (rounded to two decimals): 5, 8, 10, 12, 15

11.60

Fund X has a mean return of 12.43 percent with a standard deviation of 14.5 percent. What is the coefficient of variation for Fund X?

116.65

A sample of 100 bank customer waiting times revealed that x = 8 minutes and s = 2 minutes. Assuming that the population is normally distributed, the empirical rule states that almost all customers will have to wait between ______ and _____ minutes.

2 and 14

Determine the variance of the following sample (rounded to two decimals): 157, 132, 109, 145, 125, 139

276.70

Calculate the median of the following set of measurements: 1, 8, 1, 6, 3, 1, 8

3

Determine the standard deviation of the following population (rounded to two decimals): 5, 8, 10, 12, 15

3.41

A population has a mean of 45 and a standard deviation of 17. Which of the following population values will have negative z scores?

33 12 9

Calculate the mean of the following sample data: 1, 1, 1, 3, 6, 8, 8

4

A population has a mean of 50 and a standard deviation of 12. According to the empirical rule, approximately what percentage of the population data are contained between 38 and 62?

68%

The range of the data set 2, 5, 5, 7, and 10 is .

8

Calculate the mean of the following population data: 9, 8, 10, 10, 12, 6, 11, 10, 12, 8

9.6

Using Chebyshev's Theorem, at least ______ of the population measurements lie within 4 standard deviations of the mean.

93.75%

Identify the type of graphical model shown:

A box-and-whiskers display

Calculate the z score for the population value 7 where μ = 5 and σ = 2. z-score =

Blank 1: 1.

True or false: In the formula for calculating sample variance, the denominator is n (the sample size).

False

The interquartile range is the difference between which two quartiles?

First and third

Which of the following symbols is used to denote median?

Md

In a neighborhood there are five houses listed for sale for the following amounts: $250,000, $275,000, $280,000, $295,000, and $515,000. What is the best measure of central tendency for the price of a house in the neighborhood?

Median

Which of the following symbols is used to denote mode?

Mo

On which population distributions can the empirical rule be used?

Normal distributions Mound-shaped distributions showing not much skew in either direction.

Which of the following definitions are true?

Population standard deviation is the square root of the population variance. Population variance is the average of the squared deviations from the population mean.

Which measure of central tendency is the same as the second quartile?

The median

The coefficient of variation for Fund Z is 77.34. What does this mean?

The standard deviation is 77.34 percent of the mean.

True or false: A box-and-whiskers display is a visual representation of the Five Number Summary.

True

Chebyshev's theorem states that for a population with a mean μ and standard deviation σ, ______ 100(1−(1/k2)) percent of the population measurements lie in the interval [μ ± kσ]

at least

A ______ is a graphical summary of a data set's quartiles and interquartile range.

box-and-whiskers display

In a symmetrical t distribution, the mean is:

equal to the median and mode

For populations that are positively or negatively skewed, the empirical rule tends to ______.

give unreliable descriptions of the distribution.

The population ______ is the average of the population measurements.

mean

For a normally distributed population, 68.26% of measurements are within plus or minus standard deviations of the mean.

one

Standard deviation (the square root of variance) is expressed in _____ units as the original population.

the same

Population is the average of the squared deviations from the population mean.

variance or variation

Which of the following symbols is used to denote sample mean?

x

A population value, x, has a z score of 3. What does this mean?

x is 3 standard deviations above the mean.

Which of the following symbols is used to denote population mean?

μ

Match each measure of variation with its mathematical symbol.

σ matches Choice, population standard deviation σ2 matches Choice, population variance

Given the following sample of ten numbers: 1, 4, 2, 5, 4, 4, 6, 4, 2, 1 The mode is 4. This is because:

4 occurs most frequently in the data set

For a given population, assume the population variance is 25. The population standard deviation is equal to .

5

Given the following sample of ten numbers: 1, 4, 2, 5, 4, 4, 6, 4, 2, 1 Compute the range of the data set:

5

Calculate the 25th percentile for the following measurements: 3, 5, 7, 8, 9, 11, 13, 15

6

Arrange the steps (from first to last) to create a box-and-whiskers display.

1. Calculate Q1, Md, and Q3 2. Draw a box that extends from Q1 to Q3. Draw a vertical line through the box at Md 3. Mark the values of the lower and upper limits 4. Draw the whiskers 5. Plot the outliers

Calculate the 80th percentile for the following measurements: 3, 5, 7, 8, 9, 11, 13, 15

13

Pat's exam score placed Pat in the 85th percentile. This means that % of students scored higher than Pat.

15, 15%, fifteen, or fifteen percent

Determine the standard deviation of the following sample (rounded to two decimals): 157, 132, 109, 145, 125, 139

16.63

Fund Y has a mean return of 22.1 percent with a standard deviation of 3.73 percent. What is the coefficient of variation for Fund Y?

16.88

Match the following quartiles to their equivalent statistics:

1st Quartile matches Choice, 25th Percentile 2nd Quartile matches Choice, Median 3rd Quartile matches Choice, 75th Percentile

Given the following sample of ten numbers: 1, 4, 2, 5, 4, 4, 6, 4, 2, 1 Compute the following: Md=

4

The empirical rule tends to give unreliable estimations when for populations that are:

Negatively skewed Positively skewed

In a box-and-whiskers display, the lower whisker is drawn from ____ to _____.

Q1; the smallest measurement that is not outlying.

Which of the following statements about population variance and standard deviation are true?

The more spread out the measurements in a data set are, the larger the standard deviation will be. The raw deviations from the mean sum to zero. The more spread out the measurements in a data set are, the larger the variance will be.

For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements are _____ the value.

less than or equal to

The sample ______ is the average of the sample measurements.

mean

Which measure of central tendency is calculated by adding up all the measurements and then dividing by the number of measurements?

mean

The measure of central tendency that divides a population or sample into two roughly equal parts, is the ______.

median

A population ______ is a number calculated using the population measurements that describes some aspect of the population.

parameter

A(n) ______ is a value obtained from a sample that can be used to estimate a similar value from the larger population.

point estimate

Looking at the provided box-and-whiskers display, we can conclude that the population is probably ______.

positively skewed

Match each measure of variation with its mathematical symbol.

s matches Choice, sample standard deviation s2 matches Choice, sample variance

The sample standard deviation can be found by ________________ the sample variance.

taking the square root of

The length of the interval that contains the middle 50% of measurements is known as ______.

the interquartile range

A sampling of prices for new and used houses found that the mean price for a new house is $120,000 and the standard deviation is $6100. It also found that the mean price for a used house is $50,000 and the standard deviation is $3150. Which of the following statements are true?

The coefficient of variation for new houses is 5.08% The coefficient of variation for used houses is 6.30%