Question 1

Which of the following is a measure of variability?

Accepted Answer

Range is a measure of the spread or variability of a set of scores. It is the difference between the highest score and the lowest score in a distribution. The other options are measures of central tendency.

Question 2

Given the following distribution-24,19,15,18,16,24,17-the score that best represents the mean is

Accepted Answer

To find the mean, we add up all the scores and divide by the number of scores. 
(24 + 19 + 15 + 18 + 16 + 24 + 17) / 7 = 133 / 7 = 19
Therefore, the score that best represents the mean is 19.

Question 3

Nia has collected her dissertation data that tests a prediction model of student retention of international college students. She finds that in students from China, the predictor variables have much less variance than the same variables in students from European countries. Given this information, what can you conclude regarding the data set?

Accepted Answer

The answer of Nia has collected her dissertation data that...

Question 4

In her normally distributed achievement test scores, Lee's mean score is a 64 with a standard deviation of 6. What score would a student with a z score of 2 have on the test?

Accepted Answer

To find the score that corresponds to a z score of 2, we use the formula: 
z = (x - μ) / σ

Substituting the given values, we get: 
2 = (x - 64) / 6

Solving for x: 
x - 64 = 12 
x = 76

Therefore, a student with a z score of 2 would have a score of 76 on the test.

Question 5

Pete lives in a very demographically diverse community. Interestingly incomes are either quite high or quite low with few 'average' incomes in his town. He is conducting a survey regarding opinions about access to medical care. When he considers the variable 'income' in his data, which of the following is he most likely to report?

Accepted Answer

Because incomes in Pete's community are either quite high or quite low, there will be a large number of outliers on either side of the distribution. Therefore, the mean could be heavily influenced by those outliers and may not be a good representation of the typical income in the community. The mode is unlikely to be useful in this case because there is no clear peak in the income distribution. The range alone would not provide information about the typical income or how the income is distributed in the community. On the other hand, the median would provide a useful summary of the income distribution because it is less affected by outliers and would give a reasonable estimate of the typical income in the community.

Question 6

Given a T score of 80, the z score would be

Accepted Answer

T scores have a mean of 50 and a standard deviation of 10. A T score of 80 is 3 standard deviations above the mean, because (80-50)/10 = 3. Z scores have a mean of 0 and a standard deviation of 1, so a score 3 standard deviations above the mean is a Z score of 3.

Question 7

Griffin conducted a poll of his eighth grade class. He would like to determine how many would rather go to an amusement park versus a water park for the class trip. Which of the following is Griffin most likely to report to his peers?

Accepted Answer

Griffin is likely to report the total responses by category (amusement park vs. water park) to show which option is more popular among his classmates. This method directly compares the number of votes for each option.

Question 8

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. Which of the following best represents Claus's z score?

Accepted Answer

The z score is calculated by subtracting the mean from the raw score and then dividing by the standard deviation: $z = \frac{(86 - 88)}{4} = -\frac{2}{4} = -0.5$.

Question 9

Given the following distribution-24,19,15,18,16,24,17-the score that best represents the mode is

Accepted Answer

Mode is the number that appears most frequently in a set of data. In this distribution, the number 24 appears twice, which is more than any other number. Therefore, the mode is 24.

Question 10

Given the following distribution-24,19,15,18,16,24,17-the score that best represents the median is

Accepted Answer

The median is the middle value in a distribution, so we need to put the scores in order from least to greatest: 15, 16, 17, 18, 19, 24, 24. The middle value is the average of the two middle scores when there is an even number of scores, which in this case is (17 + 18)/2 = 17.5. However, since the scores are all whole numbers, we cannot have a decimal for the median. Therefore, we must round up to the next whole number, which is 18. Thus, the score that best represents the median is 18 (choice B).

Question 11

Maricella has collected her thesis data that examines differences in PSAT Math achievement in Latino boys and girls. However, upon a second look at the graphs of her raw scores, it appears that the boys scores are more normally distributed and the girls scores are somewhat more bunched together around the mean. Given this information, what can you conclude regarding the data set?

Accepted Answer

A smaller standard deviation means that the data is more tightly clustered around the mean, which is what is observed in the girls' distribution.

Question 12

Betsy is reporting the results of standardized testing to parents of her class students. Natal received a T score of 80. What is an accurate statement that Betsy might make to Natal's parents.

Accepted Answer

T scores have a mean of 50 and a standard deviation of 10. A T score of 80 is significantly above the mean, indicating that Natal scored at the highest end of the distribution of scores.

Question 13

Peter, a sixth-grade mathematics teacher, recently administered an exam. He wants to report a measure of central tendency but he doesn't know what to do with the fact that two students have much lower scores than anyone else. What is the best measure of central tendency for Peter to report?

Accepted Answer

The median is the best choice of central tendency because it is not affected by extreme values or outliers in the data set. Since two students have much lower scores than anyone else, they would be considered outliers and could skew the mean towards a lower value. Therefore, the median, which is the middle value when the scores are arranged in order, would give a more representative measure of the typical score for the class. Range and standard deviation are measures of variability, not central tendency.

Quiz 17: Descriptive Statistics