BUSI 2305 | Chapter 3

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

true

The median would be a better measure for the center of the data for of which of the following data sets? a. {9, 11, 14, 16, 1, 12, 15, 17} b. {0.9, 1.2, 2.2, 1.6, 2.1, 3} c. {4, 6, 5, 8, 3, 4, 7, 5} d. {6, 6, 6, 7, 7, 8, 8, 8, 8, 9}

{9, 11, 14, 16, 1, 12, 15, 17} Reason: The value {1} is much smaller than the rest of the data.

According to Chebyshev's theorem, what proportion of values for a bimodal distribution will be found within two standard deviations of the mean?

3/4

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% Reason:The waiting time of the patients in the emergency room between 1 hour and 2 hours is correct if it lies within plus and minus three standard deviations of the mean. x( with line on top) − 3s=90−(3*10)=60 = 1 hour x( with linen top) +3s=90+(3*10)=120=2 hours Therefore, approximately 99.7% of the emergency room patients will wait between 1 hour and 2 hours.

Which of the following are advantages of the variance compared to the range? Check all that apply. a. t is not unduly influenced by large or small values. b. It measures spread and center of data. c. It uses all of the values in the data, not just two. d. It is simpler to understand and calculate.

a, c

Which of the following statements are reasons to study the dispersion of data? Select all that apply. a. It allows us to compare the spread in two or more distributions. b. It allows us to compare the central values of two or more distributions. c. A small value for dispersion indicates that the data is closely clustered around the center. d. It lets us compare the number of observations in two or more sets of data.

a, c

a. Daily temperatures in August for the past 10 years b. Color of cars c. Time to run a marathon d. Finishing position in a marathon (1st, 2nd, 3rd, ...)

a, c

What does a measure of dispersion tell us about a set of data? a. It tells us about the spread of the data. b. It tells us how fast the values change within the set of data. c. It describes the central tendency of the data. d. It tells us the distance between adjacent values in the data.

a. It tells us about the spread of the data.

How do you find the Population Mean for a set of data? a. Sum the values in the population and then divide by the number of values in the population. b. Arrange the values in rank order and select the one in the middle. c. Take the number of objects in the population and divide by the sum of all the values.

a. Sum the values in the population and then divide by the number of values in the population.

When you calculate the sample mean, you divide the sum of the values in the sample by a. the number of values in the sample. b. the number of non-repeating sample values. c. the sample number minus one.

a. the number of values in the sample.

Which of the following are important properties of the arithmetic mean? Check all that apply. a. The mean can be calculated for nominal data. b. Σ(X-XX)=0 i.e. the sum of the deviations is zero. c. All of the values in the data are used in calculating the mean. d. The mean is always less than the median. e. There is only one mean for a set of data.

b, c, e

What is another term for the "average" value of a distribution? a. The normal value b. The measure of dispersion c. The distribution peak d. A measure of location

d. A measure of location

What is the purpose of a measure of location? a. To measure the shape of a distribution. b. To indicate the upper and lower values in a data set. c. To show where a specific value is located in a set of data. d. To indicate the center of a distribution of data.

d. To indicate the center of a distribution of data.

Which one of the following is a statistic? a. the range of a population b. the median of a population c. the average of a population d. the mean of a sample

d. the mean of a sample

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

sample size

Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply. a. The Empiricial Rule works for any distribution. b. Only Chebyshev's applies to skewed distributions. c. Chebyshev's theorem applies only to symmetrical, bell-shaped distributions. d. The Empirical Rule gives more precise answers for the symmetrical, bell-shaped distribution.

b, d

Which statement best describes the difference between the formula for Population and Sample variance? a. The sample variance tends to overestimate the population variance, and dividing by n-1 corrects this. b. For the sample variance, dividing by n-1 corrects a tendency to underestimate population variance. c. For population variance, dividing by N gives a better estimate of of the actual deviation.

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

In the library of a small town, the mean cost of new books is the same as the median cost of new books. The distribution of book costs is: a. negatively skewed b. symmetrically distributed c. positively skewed

b. symmetrically distributed

How does the formula for the sample mean differ from the formula for population mean? a. For sample mean, the sum of values is divided by the number of values minus one. b. To calculate the sample mean, you divide by the sample number plus one. c. The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

c. The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

Which of the following is an advantage of the range compared to the variance? Check all that apply. a. It measures spread and center of data. b. It is not unduly influenced by large or small values. c. It uses all of the values in the data, not just two. d. It is simpler to understand and calculate.

d. It is simpler to understand and calculate.

Chebyshev's Theorem states that the proportion of values is at least 1-1/k2. What is the meaning of k? a. k is the number, greater than one, found by counting the standard deviations between the sample and population. b. k is the number of observations required for a sample that will give a good population estimate. c. k is the number of standard deviations, greater than 1, within which that proportion of observations will be found.

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

The Population Mean is: a. the median value of the observations in the population b. the most common value in the population c. the arithmetic mean of all of the values in the population d. is pronounced "moo" (like the sound a cow makes)

c. the arithmetic mean of all of the values in the population

What does N represent in the formula for the population variance? a. The number of observations in the population b. The sample size c. The arithmetic mean of the population

a. The number of observations in the population

Which of the following kinds of data can be used to find a median value? a. Nominal level data b. Interval level data c. Ordinal level data d. Ratio level data

b,c,d

Which one of the following is true for a positively skewed distribution? a. There are more observations below the mode than above it. b. A small number of observations are much larger in value than most of the data. c. There are more positive observations than negative observations.

b. A small number of observations are much larger in value than most of the data.

A statistic is: a. a characteristic of a population b. a characteristic of a sample c. the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions

b. a characteristic of a sample

Which statement is true with regard to differences in the formula for the population and samples variances? a. Subtracting one from the denominator of the mean corrects for sampling error. b. Since the population size, N, is larger than the sample size, n, the sample variance is N/n times the population variance. c. The sample variance measures deviations from the sample mean, whereas the population variance uses the population mean.

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

Sample standard deviation is:

the square root of sample variance