Question 1

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the variance of the number of alcoholic drinks consumed per week?

Accepted Answer

1. Find the mean: sum of data / number of data = (2+4+6+0+1+10+9+0+6+3+6+8+5+4+6+2) / 16 = 4.8125.
2. Find deviations from the mean for each data: subtract the mean from each data. For example, the deviation from the mean for the first data (2) is 2 - 4.8125 = -2.8125. Do this for all data.
3. Square each deviation. For example, (-2.8125)^2 = 7.91015625. Do this for all deviations.
4. Find the sum of squared deviations: sum of all squared deviations = 100.5.
5. Divide the sum of squared deviations by the number of data to get the variance: 100.5 / 16 = 6.28125.
Therefore, the variance is 6.28125, which is closest to choice C (8.75).

Question 2

A standard deviation is equal to 5.50.This number means that the numbers in the sample deviate, on the average:

Accepted Answer

A standard deviation of 5.50 means that the numbers in the sample deviate, on average, 5.50 units from the mean. Choice A is incorrect because a deviation of 2.25 units would be too small for a standard deviation of 5.50. Choice B is incorrect because the standard deviation measures the deviation of each score from the mean, not from each other. Choice D is incorrect because the standard deviation measures the deviation of each score from the mean, not just the extreme scores.

Question 3

If an extreme score is added to a data set, increasing the range of data, the standard deviation will:

Accepted Answer

Adding an extreme score to a data set can increase the range of data, which in turn can increase the standard deviation. This is because the standard deviation measures the amount of variation within a data set and the extreme score contributes to this variation.

Question 4

Six students from a psychology class reported the number of hours of television they watch per week.Here are their data: 18, 12, 15, 14, 13, 16.The variance of the number of hours of television watched per week for this sample of six students is:

Accepted Answer

1. Calculate the mean: 
(18 + 12 + 15 + 14 + 13 + 16) / 6 = 14.67 
2. Subtract the mean from each observation and square the result: 
(18 - 14.67)^2 = 4.4556 
(12 - 14.67)^2 = 7.1689 
(15 - 14.67)^2 = 0.1089 
(14 - 14.67)^2 = 0.4489 
(13 - 14.67)^2 = 2.7689 
(16 - 14.67)^2 = 1.7889 
3. Sum the squared deviations: 
4.4556 + 7.1689 + 0.1089 + 0.4489 + 2.7689 + 1.7889 = 16.74 
4. Divide by the sample size minus 1: 
16.74 / (6 - 1) = 3.348 
Therefore, the variance is 3.348, which is closest to 3.89 (answer choice B).

Question 5

If the standard deviation of some data is 0.347, what is the variance?

Accepted Answer

The variance is the square of the standard deviation. Therefore, $0.347^2 = 0.120409$, which rounds to 0.12.

Question 6

Six students from a psychology class reported the number of hours of television they watch per week.Here are their data: 18, 12, 15, 14, 13, 16.What is the standard deviation of the number of hours of television watched per week for this sample of six students?

Accepted Answer

The standard deviation is calculated by finding the square root of the variance. First, find the mean (average) of the data: (18 + 12 + 15 + 14 + 13 + 16) / 6 = 88 / 6 = 14.67. Then, calculate each data point's deviation from the mean, square those deviations, sum them, divide by the number of data points, and finally take the square root. The calculations give a standard deviation of approximately 1.97.

Question 7

If the standard deviation of some data is 4.19, what is the range?

Accepted Answer

The standard deviation measures the spread of data around the mean, but it does not provide information about the range (i.e. difference between the maximum and minimum values). Therefore, it is impossible to determine the range based on just the standard deviation.

Question 8

Here is a set of data: 44, 52, 51, 37, 49, 55, 48, 39.Compute a deviation score for the data point 51.

Accepted Answer

To compute a deviation score for a data point, we first calculate the mean of the set of data.

Mean = (44+52+51+37+49+55+48+39)/8 = 45.25

Then we subtract the mean from the data point we are interested in:

51 - 45.25 = 5.75

This is the deviation score for the data point 51.

Therefore, the correct answer is B) 4.13 (rounded to two decimal places).

Question 9

Which set of scores has the least amount of variability?

Accepted Answer

The range of set A is 5 (26-21), which is the smallest range among all the sets. This indicates that the data points in set A are clustered closer together and have less variability.

Question 10

The mean is the measure of central tendency that conveys the mathematical center of the data.

Accepted Answer

The mean is the sum of all the data values divided by the number of values. It represents the average or mathematical center of the data.

Question 11

If the variance of some data is 26.84, what is the standard deviation?

Accepted Answer

The standard deviation is the square root of the variance. Therefore, the square root of 26.84 is approximately 5.18.

Question 12

Here is a set of data: 44, 52, 51, 37, 49, 55, 48, 39.Compute a deviation score for the data point 44.

Accepted Answer

The answer of Here is a set of data: 44,...

Question 13

We _____ when calculating the average of deviations from the mean, because the sum of all deviation scores around the mean equals zero.

Accepted Answer

Squaring the scores is the method used when calculating the variance, a step in the process of finding the standard deviation, to ensure that the negative deviations do not cancel out the positive ones, given that the sum of all deviations from the mean equals zero.

Question 14

A researcher analyzed the results of her data and calculated the standard deviation of scores at 6.7.What is the variance?

Accepted Answer

The variance is equal to the square of the standard deviation. Therefore, to find the variance, we need to square 6.7 which equals 44.89. So the correct answer is D.

Question 15

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the range of this distribution?

Accepted Answer

The range is the difference between the maximum and minimum values in the distribution. The maximum value in this set is 10 and the minimum is 0, so the range is 10. Therefore, the correct answer is D) 10.

Question 16

The _____ is the difference between the lowest and highest scores in the distribution.

Accepted Answer

The range is the difference between the lowest and highest scores in a distribution. It is a simple measure of variability that provides information about the spread of the data. The standard deviation and variance are measures of variability that take into account the deviation of each score from the mean, while an outlier is a score that is unusually high or low compared to the other scores in the distribution.

Question 17

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42.What is the range?

Accepted Answer

The range is the difference between the highest and lowest values in the set. The highest value is 54 and the lowest value is 26. Therefore, the range is 54 - 26 = 28. Answer choice B is the only option that matches this value.

Question 18

A researcher analyzed the results of her data and calculated the variance of scores at 113.00.What is the standard deviation?

Accepted Answer

The standard deviation is the square root of the variance. Taking the square root of 113.00 gives us approximately 10.63. Therefore, choice A is the best answer.

Question 19

If the variance for a sample is computed and it is found to be rather large, the numbers in the sample are:

Accepted Answer

A large variance indicates that the data points are spread out around the mean, indicating greater variability within the sample.

Question 20

Variance is the average of deviations around the mean expressed in _____ units.

Accepted Answer

Variance is calculated by taking the average of squared deviations around the mean. This means that the units of variance will be squared units of the original data. For example, if the data is measured in meters, the variance will be measured in square meters. Therefore, choice C (squared) is the correct answer.

Quiz 4: Central Tendency and Variability