Question 1

The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries. $\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11\
11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29 \end{array}$

Accepted Answer

The answer of The data show the total number of...

Question 2

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data.
A) $99.37
B) $98.75
C) $450
D) $250

Accepted Answer

The sample range is calculated by subtracting the smallest value from the largest value in the data set: $600 - $350 = $250.

Question 3

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data.
A) $99.37
B) $98.75
C) $450
D) $250

Accepted Answer

To calculate the sample standard deviation, first find the mean of the data: (400 + 350 + 600 + 525 + 450) / 5 = 465. Then, calculate the squared differences from the mean, sum them, divide by (n-1) where n is the sample size, and take the square root: sqrt(((400-465)^2 + (350-465)^2 + (600-465)^2 + (525-465)^2 + (450-465)^2) / 4) = $99.37.

Question 4

In symmetric distributions, the mean and the median will be approximately equal.

Accepted Answer

In symmetric distributions, the data is evenly distributed around the central point, which means that the mean and the median will be approximately equal.

Question 5

The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5. $$\begin{array} { l r r } 
& \text { Year 1 } & \text { Year 5 } \
\text { N } & 51 & 51 \
\text { MEAN } & 28.55 & 26.19 \
\text { MEDIAN } & 27.85 & 25.82
\end{array}$$ Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5.

Accepted Answer

The answer of The output below displays the mean and...

Question 6

The total points scored by a basketball team for each game during its last season have been summarized in the table below. Identify the modal class of the distribution of scores. $$\begin{array} { | c | c | } 
\hline \text { Score } & \text { Frequency } \
\hline 41 - 60 & 3 \
\hline 61 - 80 & 8 \
\hline 81 - 100 & 12 \
\hline 101 - 120 & 7 \
\hline
\end{array}$$

Accepted Answer

The answer of The total points scored by a basketball...

Question 7

The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places. 180, 100, 195, 130, 155
A) 38.1772
B) 243.3465
C) 174.0675
D) 137.11

Accepted Answer

To calculate the standard deviation, first find the mean of the speeds, then calculate the variance by finding the average of the squared differences from the mean, and finally take the square root of the variance. The standard deviation is approximately 38.1772.

Question 8

In a symmetric and mound shaped distribution, we expect the values of the mean, median, and mode to differ greatly from one another.

Accepted Answer

In a symmetric and mound shaped distribution, the mean, median, and mode are all expected to be around the same value, so they should not differ greatly from one another.

Question 9

Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 280 students and recorded how long it took each of them to find a parking spot. The times had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 280 times collected.

Accepted Answer

The answer of Parking at a university has become a...

Question 10

In skewed distributions, the mean is the best measure of the center of the distribution since it is least affected by extreme observations.

Accepted Answer

In skewed distributions, the mean can be heavily influenced by extreme values, so the median is a better measure of center.

Question 11

Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: $$\begin{array} { l r l r } 
\text { Company A } & \$ 71.4 & \text { Company F } & \$ 27.1 \
\text { Company B } & 60.1 & \text { Company G } & 25.1 \
\text { Company C } & 56.5 & \text { Company H } & 23.1 \
\text { Company D } & 55 & \text { Company I } & 22.9 \
\text { Company E } & 28.6 & \text { Company J } & 20.6
\end{array}$$ Calculate the sample variance.
A) 372.307
B) 3759.244
C) 2070.113
D) 1854.860

Accepted Answer

The sample variance is calculated as the sum of the squared deviations from the mean divided by the number of observations minus one. The mean is calculated as the sum of the observations divided by the number of observations. In this case, the mean is (71.4 + 60.1 + 56.5 + 55 + 28.6 + 27.1 + 25.1 + 23.1 + 22.9 + 20.6) / 10 = 440.4 / 10 = 44.04. The squared deviations from the mean are (71.4 - 44.04)^2 + (60.1 - 44.04)^2 + (56.5 - 44.04)^2 + (55 - 44.04)^2 + (28.6 - 44.04)^2 + (27.1 - 44.04)^2 + (25.1 - 44.04)^2 + (23.1 - 44.04)^2 + (22.9 - 44.04)^2 + (20.6 - 44.04)^2 = 1854.86. The sample variance is therefore 1854.86 / (10 - 1) = 1854.86 / 9 = 206.118.

Question 12

Calculate the range of the following data set: 9, 6, 9, 2, 8, 10, 6, 6, 9
A) 8
B) 10
C) 2
D) 12

Accepted Answer

The answer of Calculate the range of the following data...

Question 13

The mean and the median are useful measures of central tendency for both qualitative and quantitative data.

Accepted Answer

The mean and median are measures of central tendency primarily used for quantitative data. For qualitative data, the mode is a more appropriate measure.

Question 14

In practice, the population mean μ is used to estimate the sample mean x.

Accepted Answer

In practice, the sample mean x is used to estimate the population mean μ.

Question 15

In general, the sample mean is a better estimator of the population mean for larger sample sizes.

Accepted Answer

As the sample size increases, the sample mean becomes closer to the true population mean. This is due to the Central Limit Theorem, which states that as the sample size increases, the sample mean will approach a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, for larger sample sizes, the sample mean is a more precise and accurate estimator of the population mean.

Question 16

A shoe company reports the mode for the shoe sizes of men's shoes is 12. Interpret this result.
A) The most frequently occurring shoe size for men is size 12
B) Most men have shoe sizes between 11 and 13.
C) Half of the shoes sold to men are larger than a size 12
D) Half of all men's shoe sizes are size 12

Accepted Answer

The mode is the value that appears most frequently in a data set, so the most frequently occurring shoe size for men is size 12.

Question 17

Which of the following is not a measure of central tendency?
A) range
B) median
C) mode
D) mean

Accepted Answer

Range is a measure of dispersion, not central tendency.

Question 18

The calculator screens summarize a data set.  a. Identify the mean and the median. b. Based only on the mean and the median, do you expect that the data set is skewed to the right, symmetric, or skewed to the left? Explain.

Accepted Answer

The answer of The calculator screens summarize a data set....

Question 19

The ages of five randomly chosen professors are 69, 52, 55, 62, and 49. Calculate the sample variance of these ages.

Accepted Answer

The answer of The ages of five randomly chosen professors...

Question 20

The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?
A) median
B) mode
C) mean
D) range

Accepted Answer

The median is the best measure of central tendency for skewed distributions because it is not affected by extreme values, unlike the mean.

Quiz 2: Methods for Describing Sets of Data

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data.

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data.

In symmetric distributions, the mean and the median will be approximately equal.

The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places. 180, 100, 195, 130, 155

In a symmetric and mound shaped distribution, we expect the values of the mean, median, and mode to differ greatly from one another.

In skewed distributions, the mean is the best measure of the center of the distribution since it is least affected by extreme observations.

Calculate the range of the following data set: 9, 6, 9, 2, 8, 10, 6, 6, 9

The mean and the median are useful measures of central tendency for both qualitative and quantitative data.

In practice, the population mean μ is used to estimate the sample mean x.

In general, the sample mean is a better estimator of the population mean for larger sample sizes.

A shoe company reports the mode for the shoe sizes of men's shoes is 12. Interpret this result.

Which of the following is not a measure of central tendency?

The calculator screens summarize a data set. a. Identify the mean and the median. b. Based only on the mean and the median, do you expect that the data set is skewed to the right, symmetric, or skewed to the left? Explain.

The ages of five randomly chosen professors are 69, 52, 55, 62, and 49. Calculate the sample variance of these ages.

The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?