Chapter 3 - ADD

Sample standard deviation is:

The square root of sample variance.

The population standard deviation is

The square root of the population variance

Which of the following is a statistic?

The median of a population The range of a population The average of a population *The mean of a sample*

The larger the population variance is for a data set,

The more spread out the data is.

Which one of the following is true for a symmetrical distribution?

The mean, median and mode all have the same value.

Suppose the wait time at the emergency room follow a symmetrical, bell-shaped distribution with a mean of 90 minutes and a standard deviation of 10 minutes. What percentage of emergency room patients will wait between 1 hour and 2 hours?

99.7%

How is the formula for the sample variance different from that of the population variance? Select all that apply.

For the sample variance, the sample mean is used in place of the population mean. For the sample variance, the denominator is the number of observations minus 1.

What does a small value for a measure of dispersion tell us about a set of data?

It indicates that the data are closely clustered about the center.

Of the following, which one is an advantage of the standard deviation over the variance?

It is in the same units as the data.

What is the standard deviation of the following population data? 3, 1, 2, 9, 5

2.83

What is the variance of the following sample data? 8, 6, 2, 8

2.83

The variance of the following sample data? 2,6,2,10

N: 4 M: 5 SS: 44 s2 = SS⁄(N - 1) = 44/(4-1) = 14.67

According to the Empirical rule, a certain percentage of observations will be found within a specific number of standard deviations of the mean for a normal distribution. Match the percentage of observations to the number of standard deviations.

68% = plus or minus one standard deviation 95% = plus or minus two standard deviations 99.7% = plus or minus three standard deviations

The variance of the following sample data? 8,6,2,8

8.00

Chose the best definition for the variance.

The arithmetic average of the squared deviations from the mean.

The median would be a better measure for the center of the data for which of the following data sets?

(11,14,16,1,12,15,17) The value 1 is much smaller than the rest of the data.

According to Cheryshev's theorem, what proportion of observations will lie within 3 standard deviations of mean for the positively skewed distribution?

8/9; 1-1/2squared=8/9

If all the data are the same, then the population variance will be what?

0; If all then numbers are the same, then there is no variability.

Chebyshev's Theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is:

1-1/k^2 for k>1

Suppose the sample variance is calculated for a data set containing the ages, in years, of a sample of visitors to the zoo and it is 4. What is the standard deviation?

2 years; take the square root of 4

What is the standard deviation of the following sample data? 2, 6, 2, 0, 5

2.45

What is the standard deviation of the following population data? 3, 6, 2, 9

2.74

Calculate the mean for the following sample of data: 12, 15, 6, 4, 8

9; add up all the numbers, then divide by how many numbers there are = 45/5

What is the range for the following set of data? 4,12,5,3,7,8,9

9; difference between the max and min values in the data set - 12 and 3

What is the definition of "parameter?"

A characteristic of a population.

Which one of the following would be an example of a measure of location?

An average

Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that appl

Chebyshev's theorem works for symmetrical, bell-shaped distributions. Chebyshev's theorem applies to any set of values.

Which of the following are good measures of the center of an income distribution in a country where most of the households have annual incomes of about $40,000, but a small number of households have incomes above $1,000,000? Select all that apply.

Median Mode

Which of the following is true regarding medians and means?

Medians can be calculated from ordinal-level data, but means can't

What is the variance of the following population data? 2,6,1

N: 3 M: 3 SS: 14σ2 = SS⁄N = 14/3 = 4.67

What is the standard deviation of the following sample data? 7,6,2,0,5

N: 5 M: 4 SS: 34 s2 = SS⁄(N - 1) = 34/(5-1) = 8.5 s = √s2 = √8.5 = 2.92

Which of the levels of measurement can the mode be used? Select all that apply.

Nominal Ordinal Interval Ratio

Why would one use a grouped mean or standard deviation?

Only the frequency distribution data is available.

Most of the items sold at a garage sale cost about $12. Nothing sold for more than $15, but a few items cost only a few cents. Which of the following would not be a good measure of the center of the distribution of sale prices? Select all that apply.

The Standard Deviation The Mean

Which of the following statements are true of the weighted mean? Select all that apply.

The denominator of the weighted mean is always the sum of the weights. It is a special case of the arithmetic mean. It is used when there are several observations of the same value. It is used with data that has repeating values, such as frequency distribution

Which of the following accurately describes the median of a set of data?

The midpoint of the data when it is arranged in order.

When you calculate the sample mean, you divide the sum of the values in the sample by

The number of observations in the sample.

True or false: The standard deviation is a measure of dispersion.

True

What does N represent in the formula for the population variance?

number of observations in population

What does n represent in the formula for the sample variance?

sample size

How do you find the population mean for a set of data?

Divide the sum of the values in the population by the number of values in the population.

Which of the following is the correct formula for the population variance?

E(x-mu)squared over N

Which statement best describes the difference between the formula for Population and Sample variance?

For the sample variance, dividing by n-1 corrects a tendency to underestimate population variance.

Which of the following is an advantage of the mode?

It is not affected by extreme values.

Which of the following are advantages of the variance compared to the range? Check all that apply.

It is not unduly influenced by large or small values. It uses all of the values in the data, not just two.

Which of the following is an advantage of the range compared to the variance? Check all that apply.

It is simpler to understand and calculate.

Which of the following are advantages of the variance compared to the range?

It uses all of the values in the data, not just two.

Which statement is true with regard to differences in the formula for the population and samples variances?

The sample variance measures deviations from the sample mean, whereas the population variance uses the population mean.

Which of the following statements best defines the mode?

The value that is the midpoint of the data.

Given the following weights (in ounces) of four apples, 6, 8, 10 and 7, which of the following is true?

The variance would be in ounces-squared.

Which of the following are important properties of the arithmetic mean? Check all that apply.

There is only one mean for a set of data. All of the values in the data are used in calculating the mean. ...The sum of the deviation is zero.

Which one of the following is true regarding the use of the mode, mean, and median for different levels of measurement?

Only the mode can be used for nominal-level data.

Which of the following statements describe weaknesses of the range as a measure of dispersion? Select all that apply.

Only two values from the data set are used. It may be unduly influenced by an unusually large value It may be unduly influenced by an especially small value. The calculation is easy to perform

Which of the following statements describe weaknesses of the range as a measure of dispersion?

Only two values from the data set are used. It may be unduly influenced by the especially small value. I may be unduly influenced by an unusually large value.

Which of the following kinds of data can be used to find a median value? Select all that apply.

Ordinal level data Interval level data Ratio level data

Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply.

The Empirical Rule gives more precise answers for the symmetrical, bell-shaped distribution. Only Chebyshev's applies to skewed distributions.

How does the formula for the sample mean differ from the formula for population mean?

The Greek letter mu, is used to represent the population with, x-bar is used for the sample mean. The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size)

Which measure of dispersion results in units that are different from the data?

Variance

Which of the following are used to measure dispersion? Check all that apply.

Variance, Range and Standard Deviation

What characteristic of a data set makes the median the better measure of the center of the data than the mean?

When the data set includes one or two very large or very small values.

In a certain neighborhood most of the houses cost about $60,000 and the median cost is $76,000. One house cost $700,000 and the mean cost was $82,500. The distribution of housing costs is:

Positively skewed

In a particular country most of the households have an annual income of about $20,500. Five percent of the households have incomes above $500,000. The distribution of income is:

Positively skewed

Suppose a data set includes 11 values. Which one would be the median?

The 6th value in the ordered listing of the data.

Which one of the following is an unethical approach to reporting statistics?

Giving only the measures of location and dispersion that support your point of view.

Which of the following statements are reasons to study dispersion of data? Select all that apply.

It allows us to compare the spread in two or more distributions.

Chebyshev's Theorem states that the proportion of values is at least 1-1/k2. What is the meaning of k?

k is the number of standard deviations, greater than 1, within which that proportion of observations will be found.

Which of the following is an advantage of the compared to the variance?

simpler to understand calculate uses all values in data, not just two not unduly influenced by large or small numbers