Statistics Chapter 3

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

- 12, 14, 15, 12, 14, 13 - Because it is the most spread out.

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% - 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⎯⎯−3s=90−(3*10)=60 = 1 hourx⎯⎯+3s=90+(3*10)=120=2 hoursx¯-3s=90-(3*10)=60 = 1 hourx¯+3s=90+(3*10)=120=2 hours - Therefore, approximately 99.7% of the emergency room patients will wait between 1 hour and 2 hours.

What is the purpose of a measure of location?

- To indicate the center of distribution of data

True or false: The variance is a measure of central tendency.

- (False)

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

- (True) - The range, variance and standard deviation are all measures of dispersion

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

- A small value for dispersion indicates that the data is closely clustered around the center. - It allows us to compare the spread in two or more distributions.

The mean, median, and mode are all the same for which type of distribution?

- A symmetrical distribution.

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

- All of the values in the data are used in calculating the mean. - There is only one mean for a set of data. - Σ(X-XX)=0 i.e. the sum of the deviations is zero.

Which of the following are disadvantages of the mode?

- For many sets of data there are multiple modes. - For many sets of data there is no mode.

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.

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

- It indicates that the data is closely clustered around 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 does a measure of dispersion tell us about a set of data?

- It tells us about the spread of the data

The formula for the weighted mean is.... Which of the following statements are true of the weighted mean? Select all that apply.

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

What is another term for the "average" value of a distribution?

- Measure of location

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.

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.

For which of the following variables can one calculate the arithmetic mean?

- Time to run a marathon - Daily temperatures in August for the past 10 years

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

- Variance

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.

The larger the population variance is for a data set,

- the more spread out the data is

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

- the number of values in the sample.

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

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

Why is it important to consider measures of dispersion as well as measures of location when reporting statistics?

- Measures of location do not tell us about the spread or clustering of data.

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

- The formulas are functionally the same, but "n" (the sample size) is used instead of "N" (the population size)

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

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

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

- The number of observations in the population

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

- The sample size