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

Suppose a population is made up of the following values: 1, 8, 5, 6. What is the population mean?

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%
• 95%
• 99.7%

• Plus or minus one standard deviation.

• Plus or minus two standard deviation.

• Plus or minus three standard deviation.

Which of the following are important properties of the arithmetic mean?

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

What is the definition of "parameter"?

A characteristic of a population.

How is the formula for the sample variance different from that of the population variance?

• 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.

The difference between the largest and the smallest values in a data set is called the _____.

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

• The Greek letter mu, *u*, is used to represent the population while, *X*, 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).

a characteristic of a sample

Which of the following are used to measure dispersion?

• Variance
• Standard deviation
• Range

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

The median is defined as:

the midpoint of the values after they have been arranged in rank order

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

The sample standard deviation is the square root of the sample variance.

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.

Choose the best definition for the variance.

The arithmetic average of the squared deviations from the mean.

Which of the following statements is true of the weighted mean?

• It is a special case of the arithmetic mean

• The denominator of the weighted mean is always the sum of the weights

• It is used when there are several observations of the same value

• It is used with data that has repeated values, such as a frequency distribution.

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

• The Empirical Rule give more precise answers for the symmetrical, bell-shaped distribution.

• Chebyshev's theorem works for symmetrical, bell-shaped distributions.

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

For which of the levels of measurement can the mode be used?

• Ordinal
• Ratio
• Nominal
• Interval

Which of the following statements best defines the mode?

The value of the observation that appears most frequently.

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 an unusually large value.

• It may be unduly influenced by an especially small value.

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

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

What is the variance of the following population data?

2, 0, 1, 9

12.5

Explanation:

1. Begin by finding the mean.
2. Find the difference between each observation and the mean, and square that difference.
3. Sum all the squared differences.
4. Divide the sum of the squared differences by the number of items in the population.

1. 2+0+1+9 = 12 / 4 = 3
2. (2-3)^2 = 1, (0-3)^2 = 9, (1-3)^2 = 4, (9-3)^2 = 36
3. 1+9+4+36 = 50
4. 50/4 = 12.5

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

It is in the same units as the data.

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:

Which of the following kinds of data can be used to find a median value?

• Interval
• Ratio
• Ordinal

Not:

• Nominal

Which of the following are reasons why the mode would not be the good choice of measure for describing the center of a set of data?

• There may be no observation that occurs more than once.

• The data may be bimodal. (meaning there is two modes)

• The most frequent observation is much higher or much lower than most of the data values.

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.

What is the standard deviation of the following population data?

3, 1, 2, 9, 5

1. Begin by finding the mean.
2. Find the difference between each observation and the mean, and square that difference.
3. Sum all the squared differences.
4. Divide the sum of the squared differences by the number of items in the population.
5. Take the square root.

2.83

*Refer to early flashcard for process* (Population Variance card)

Given the following population data sets, which has a smaller population variance?

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 distribution of the sale prices?

• the standard deviation

• the mean

What is the standard deviation of the following sample data?

2, 6, 2, 0, 5

In the library of a small town, the mean cost of new books is the same as the median and mode cost of new books. The distribution of book costs is:

Symmetrically distributed

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 for the following sample set?

8, 6, 2, 8

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

What is the standard deviation of the following sample data?

7, 6, 2, 0, 5

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}

Explanation:

The value 1 is much smaller than the rest of the data

Which of the following is an advantage of the mode?

It is not affected by extreme values.

The average age of undergraduate students at Grand Canyon University is 44. If the standard deviation is 4, what percentage of undergraduate students are between 36 and 52 years old?

75%

Not:

89%

This would be true if k=3, but k=2 because (36-44)/4 = -2 and (52-44)/4 = 2

Which of the following statements are reasons to study the dispersion of data?

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

In a certain neighborhood most of the houses cost $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:

Give 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

Find the median for the following sample of data: 3, 2, 7, 5, 6.

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

What characteristics 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.

Explanation:

Extreme values impact the mean much more than the median.

Not:

When the data set includes one or two values that are repeated several times.

Explanation:

The presence of recurring values does not make the median preferred.

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 around the center.

Chebyshev's theorem states that the proportion of values is at least 1-1/k^2. What is the meaning of k?

For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1-1/k^2, where k is any value greater than 1.

Compute the mean of the following population of values:

5, 7, 6, 5, 6

The Cambridge Power and Light Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar amount, the customers were charged for electrical services last month:

50 78 60 52 22 42 75 45 63 54

78 68 54 28 48 75 42 68 44 62

A. Compute the arithmetic mean.

B. Indicate whether it is a statistic or a parameter.

In June, an investor purchased 300 shares of Oracle (an information technology company) stock at $40 per share. In August, she purchased an additional 290 shares at $37 per share. In November, she purchased an additional 530 shares at $45 per share. What is the weighted mean price per share?

$41.59

Explanation:

300x$40=$12,000

290x$37=$10,730

530x$45=$23,850

$12,000+$10,730+$23,850=$46,580

$46,580/1120=$41.589

The personnel files of all eight employees at the Pawnee location of Acme Carpet Cleaners Inc. revealed that during the last 6-month period they lost the following number of days due to illness:

0 6 2 5 2 2 3 5

All eight employees during the same period at the Chickpee location of Acme Carpets Cleaners revealed they lost the following number of days due to illness:

0 1 0 3 2 2 10 2

A. Calculate the range and mean for the Pawnee location and the Chickpee location.

Pawnee Location

• Range:
• Mean

Chickpee Location

• Range
• Mean

B-1 Based on the sample data, which location has fewer lost days?

B-2 Based on the sample data, which location has less variation?

A.

Pawnee Location

Range: 6

Mean: 3.13

Chickpee Location

Range: 10

Mean: 2.5

B-1:

Chickpee location

B-2:

Pawnee location

The annual report of Dennis Industries cited these primary earnings per common share for the past 5 years: $2.38, $1.41, $2.06, $4.16, and $5.96. If we assume these are population values.

A. What is the arithmetic mean primary earnings per share of common stock?

B. What is the variance?

The ages of a sample of Canadian tourists flying from Toronto to Hong Kong were 26, 23, 58, 46, 50, 17, 73, 50, 30, and 41.

A. Compute the range.

B. Compute the standard deviation

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

717 681 735 725 719 721 737 698 718 759 681 699 696

716 719 722 733 720 690 691 768 709 736 761 687

A. Find the mean, median, and mode of this information.

B. What are the range and standard deviation?

C. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations.

A.

Mean: 717.52

Median: 719

Mode: 681 and 719

B.

Range: 87

Standard Deviation: 24.02

C.

669.48-765.56