Question 1

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 2

Calculate the variance of a sample for which $n = 5 , \sum ^ { 2 } = 1320 , \sum ^ { x } = 80$
A) 8.00
B) 3.16
C) 10.00
D) 326.00

Accepted Answer

The variance of a sample is calculated using the formula $s^2 = \frac{\sum x^2 - (\sum x)^2 / n}{n - 1}$. Plugging in the given values, we get $s^2 = \frac{1320 - (80)^2 / 5}{5 - 1} = \frac{1320 - 1280}{4} = \frac{40}{4} = 10.00$.

Question 3

Compute $\mathrm { s } ^ { 2 }$ and s for the data set: -3,-1,-4,-3,1,-3
A) 2.24 ; 1.5
B) 1.87 ; 1.37
C) 3.37 ; 1.83
D) 32.3 ; 5.68

Accepted Answer

The variance ($\mathrm { s } ^ { 2 }$) and standard deviation (s) for a sample can be calculated using the formulas for sample variance and standard deviation. First, find the mean of the data set: $\frac{-3 - 1 - 4 - 3 + 1 - 3}{6} = \frac{-13}{6} = -2.17$. Then, calculate the sum of the squared differences from the mean: $\sum (x_i - \bar{x})^2 = (-3 + 2.17)^2 + (-1 + 2.17)^2 + (-4 + 2.17)^2 + (-3 + 2.17)^2 + (1 + 2.17)^2 + (-3 + 2.17)^2 = 3.37$. Divide by $n-1$ (where $n$ is the number of data points) to get the variance: $\frac{3.37}{6-1} = 3.37$. The standard deviation is the square root of the variance: $\sqrt{3.37} = 1.83$.

Question 4

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: $$\begin{array} { l r l l } 
\text { Company A } & \$ 72 & \text { Company F } & \$ 27.3 \
\text { Company B } & 63.6 & \text { Company G } & 25 \
\text { Company C } & 57.3 & \text { Company H } & 23.8 \
\text { Company D } & 54 & \text { Company I } & 23.1 \
\text { Company E } & 31.1 & \text { Company J } & 19.2
\end{array}$$ Calculate the sample variance.
A)391.238
B)3883.082
C)1919.040
D)2141.564

Accepted Answer

The sample variance is calculated as the sum of the squared deviations from the mean divided by the sample size minus one. The mean is calculated as the sum of the values divided by the sample size. In this case, the mean is (72 + 63.6 + 57.3 + 54 + 31.1 + 27.3 + 25 + 23.8 + 23.1 + 19.2) / 10 = 400 / 10 = 40. The squared deviations from the mean are (72 - 40)^2 + (63.6 - 40)^2 + (57.3 - 40)^2 + (54 - 40)^2 + (31.1 - 40)^2 + (27.3 - 40)^2 + (25 - 40)^2 + (23.8 - 40)^2 + (23.1 - 40)^2 + (19.2 - 40)^2 = 1024 + 518.4 + 302.5 + 196 + 78.4 + 169 + 225 + 262.4 + 285.6 + 435.6 = 3912.5. The sample variance is therefore 3912.5 / (10 - 1) = 3912.5 / 9 = 434.722.

Question 5

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. $$\begin{array} { c c c c c c c c c } 
1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \
11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29
\end{array}$$

Accepted Answer

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

Question 6

Calculate the range of the following data set: 8, 7, 9, 1, 6, 10, 4, 7, 4
A)1
B)10
C)11
D)9

Accepted Answer

The range is calculated by subtracting the smallest value (1) from the largest value (10) in the data set, resulting in a range of 9.

Question 7

The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?
A)99
B)cannot be determined
C)70.5
D)78

Accepted Answer

The highest score can be determined by adding the range to the lowest score: 57 + 42 = 99.

Question 8

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)$98.75
B)$99.37
C)$250
D)$450

Accepted Answer

The sample range is calculated by subtracting the smallest value in the sample from the largest value. Here, the largest value is $600 and the smallest is $350, so the range is $600 - $350 = $250.

Question 9

The temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following could be calculated using just this information?
A)median
B)range
C)variance
D)standard deviation

Accepted Answer

The range of a set of data is the difference between the highest and lowest values, which can be calculated using just the given temperatures (89°F - 73°F). Median, variance, and standard deviation require more specific data points within the range.

Question 10

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

Accepted Answer

In symmetric distributions, the distribution is mirrored around a central point, meaning the mean (average value) and the median (middle value) will fall at the same point or very close to each other, making them approximately equal.

Question 11

In practice, the population mean $\mu$ is used to estimate the sample mean $\bar { x }$

Accepted Answer

In practice, the sample mean $\bar{x}$ is used to estimate the population mean $\mu$, not the other way around.

Question 12

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 tends to be closer to the population mean due to the Law of Large Numbers, making it a better estimator.

Question 13

Compute $\mathrm { s } ^ { 2 }$ and s for the data set: $\frac { 1 } { 10 } , \frac { 3 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 5 } , \frac { 7 } { 10 } , \frac { 3 } { 10 } .$
A) 0.033 ; 0.183
B) 6.667 ; 2.582
C) 0.767 ; 0.876
D) 0.067 ; 0.258

Accepted Answer

To compute the sample variance ($\mathrm { s } ^ { 2 }$) and the sample standard deviation (s) for the given data set, we first find the mean of the data set, then use the formula for sample variance and finally take the square root of the variance to find the standard deviation. The correct computation leads to a sample variance ($\mathrm { s } ^ { 2 }$) of 0.067 and a sample standard deviation (s) of 0.258.

Question 14

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 equal or very close to each other, not differing greatly.

Question 15

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)$250
B)$450
C)$99.37
D)$98.75

Accepted Answer

The sample standard deviation is calculated using the formula: sqrt[Σ(xi - x̄)² / (n-1)], where xi represents each value, x̄ is the mean of the sample, and n is the number of observations. First, find the mean: (400 + 350 + 600 + 525 + 450) / 5 = 465. Then, calculate each deviation from the mean, square it, sum those squares, divide by n-1 (which is 4), and finally take the square root. Doing this gives a sample standard deviation of approximately $99.37.

Question 16

The ages of five randomly chosen professors are 47, 55, 52, 63, and 66. Calculate the
sample variance of these ages.

Accepted Answer

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

Question 17

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.
195, 135, 200, 190, 150
A)276.6903
B)29.4534
C)196.6443
D)155.51

Accepted Answer

The standard deviation is calculated by finding the mean (average) speed first, which is (195 + 135 + 200 + 190 + 150) / 5 = 174. Then, for each speed, subtract the mean and square the result, sum these squared differences, divide by the number of speeds (5), and finally take the square root. The calculation gives a standard deviation of 29.4534.

Question 18

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 median is often considered a better measure of the center because it is less affected by extreme values than the mean.

Question 19

Calculate the standard deviation of a sample for which $n = 6 , \sum x ^ { 2 } = 830 , \sum x = 60$
A) 6.78
B) 6.19
C) 46.00
D) 164.00

Accepted Answer

The standard deviation of a sample is calculated using the formula: $s = \sqrt{\frac{1}{n-1} \left( \sum x^2 - \frac{(\sum x)^2}{n} \right)}$. Substituting the given values, $n = 6$, $\sum x^2 = 830$, and $\sum x = 60$, we get $s = \sqrt{\frac{1}{6-1} \left( 830 - \frac{(60)^2}{6} \right)} = \sqrt{\frac{1}{5} \left( 830 - 600 \right)} = \sqrt{\frac{230}{5}} = \sqrt{46} \approx 6.78$.

Question 20

The calculator screens summarize a data set.  a. Identify the smallest measurement in the data set.
b. Identify the largest measurement in the data set.
c. Calculate the range of the data set.

Accepted Answer

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

Quiz 2: Methods for Describing Sets of Data

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

Calculate the variance of a sample for which n=5,∑2=1320,∑x=80n = 5 , \sum ^ { 2 } = 1320 , \sum ^ { x } = 80n=5,∑2=1320,∑x=80

Compute s2\mathrm { s } ^ { 2 }s2 and s for the data set: -3,-1,-4,-3,1,-3

Calculate the range of the following data set: 8, 7, 9, 1, 6, 10, 4, 7, 4

The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?

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 temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following could be calculated using just this information?

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

In practice, the population mean μ\muμ is used to estimate the sample mean xˉ\bar { x }xˉ

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

Compute s2\mathrm { s } ^ { 2 }s2 and s for the data set: 110,35,110,15,710,310.\frac { 1 } { 10 } , \frac { 3 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 5 } , \frac { 7 } { 10 } , \frac { 3 } { 10 } .101​,53​,101​,51​,107​,103​.

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

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.

The ages of five randomly chosen professors are 47, 55, 52, 63, and 66. Calculate the sample variance of these ages.

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. 195, 135, 200, 190, 150

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 standard deviation of a sample for which n=6,∑x2=830,∑x=60n = 6 , \sum x ^ { 2 } = 830 , \sum x = 60n=6,∑x2=830,∑x=60

The calculator screens summarize a data set. a. Identify the smallest measurement in the data set. b. Identify the largest measurement in the data set. c. Calculate the range of the data set.

Calculate the variance of a sample for which $n = 5 , \sum ^ { 2 } = 1320 , \sum ^ { x } = 80$

Compute $\mathrm { s } ^ { 2 }$ and s for the data set: -3,-1,-4,-3,1,-3

In practice, the population mean $\mu$ is used to estimate the sample mean $\bar { x }$

Compute $\mathrm { s } ^ { 2 }$ and s for the data set: $\frac { 1 } { 10 } , \frac { 3 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 5 } , \frac { 7 } { 10 } , \frac { 3 } { 10 } .$

Calculate the standard deviation of a sample for which $n = 6 , \sum x ^ { 2 } = 830 , \sum x = 60$