Question 1

Given the following distribution-24,19,15,18,16,24,17-the score that best represents the mode is
A) 15
B) 18
C) 19
D) 24

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 2

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?
A) The standard deviation is likely smaller the Chinese students.
B) The mean is likely higher for the Chinese students.
C) The variance is likely larger for the European students.
D) The mean is likely higher for the European students.

Accepted Answer

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

Question 3

Betsy is reporting the results of standardized testing to parents of her class students. Natal received a t score of 80.
-Given Natal's t-score, his z-score would be
A) -1
B) 0
C) 2
D) 3

Accepted Answer

A t-score of 80 corresponds to a z-score of 3 because the t-score is calculated as 50 + 10*z. Solving for z when the t-score is 80 gives z = (80 - 50) / 10 = 3.

Question 4

Anton collected survey data regarding teachers' use of technology in their teaching activities. He was pleased that his data are generally normally distributed. Among other data, he collected age, number of years teaching, highest degree held, amount of time spent in online office hours weekly, and whether the teacher reported using an electronic discussion board.
-Anton will most likely report which of the following measures of central tendency for the variable highest degree held?
A) Mode
B) Range
C) Mean
D) Median

Accepted Answer

The highest degree held is a categorical variable, and the mode is the most appropriate measure of central tendency for categorical data.

Question 5

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.
A) Natal scored at the lowest end of the distribution of scores.
B) Natal scored at about the mean of the group of students taking the assessment.
C) Natal scored at the highest end of the distribution of scores.
D) Natal scored an 80% correct on the items presented on the test.

Accepted Answer

A t score of 80 is significantly above the average, indicating that Natal scored at the highest end of the distribution of scores.

Question 6

Which of the following is a measure of variability?
A) Mode
B) Range
C) Median
D) Total score

Accepted Answer

Range is a measure of variability that represents the difference between the highest and lowest scores in a dataset. Mode is a measure of central tendency, median is also a measure of central tendency, and total score is not a measure of variability.

Question 7

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?
A) 58
B) 70
C) 76
D) 80

Accepted Answer

A Z-score of 2 means the score is 2 standard deviations above the mean. With a mean of 64 and a standard deviation of 6, the score would be 64 + (2 * 6) = 76.

Question 8

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?
A) Variance in responses
B) Mean responses
C) Total responses by category
D) Mode of responses

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 9

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?
A) The standard deviation is likely smaller for girls.
B) The girls' distribution is likely unimodal.
C) The girls' mean score is more representative of the data.
D) The girls' median is higher than the boys' median.

Accepted Answer

A smaller standard deviation suggests that the values in the data set are closer to the mean, which is consistent with the girls' scores being more bunched together around the mean.

Question 10

Given the following distribution-24,19,15,18,16,24,17-the score that best represents the mean is
A) 15
B) 18
C) 19
D) 24

Accepted Answer

To find the mean of a set of numbers, you add up all the values and divide by the total number of values. In this case, the sum of the numbers is 113. Dividing by the total of 7 values gives a mean of approximately 16.14. Since none of the choices match this exact value, we want to choose the score that is closest to the mean. Looking at the distribution, we can see that 18 is the score closest to our calculated mean of 16.14, so the best choice is B.

Question 11

Anton collected survey data regarding teachers' use of technology in their teaching activities. He was pleased that his data are generally normally distributed. Among other data, he collected age, number of years teaching, highest degree held, amount of time spent in online office hours weekly, and whether the teacher reported using an electronic discussion board.
-Anton will most likely report which of the following measures of central tendency for the variable number of years teaching?
A) Mode
B) Range
C) Mean
D) Median

Accepted Answer

The variable "number of years teaching" is a continuous numerical variable and the data is generally normally distributed. In this case, the most appropriate measure of central tendency to report is the mean. The mode and median may also be reported as supplemental measures, but the mean is likely the most appropriate given the normal distribution of the data. The range is a measure of dispersion, not central tendency, and is not appropriate to report in this context.

Question 12

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?
A) Range
B) Mean
C) Median
D) Mode

Accepted Answer

Since incomes are either quite high or quite low in Pete's town, there is likely to be a skewed distribution of income data. As such, the median would be a better measure of central tendency than the mean, which can be heavily influenced by outliers. Additionally, reporting the range or mode would not be as informative in assessing opinions about access to medical care in relation to income.

Question 13

Given the following distribution-24,19,15,18,16,24,17-is best described as
A) Approximately normal
B) Bi-modally distributed
C) Negatively skewed
D) Positively skewed

Accepted Answer

The distribution is negatively skewed because the tail of the distribution is longer on the left side, with most of the scores clustered on the right side.

Question 14

Given the following distribution-24,19,15,18,16,24,17-the measure of central tendency best to report is the
A) Mean
B) Range
C) Median
D) Mode

Accepted Answer

The median is the middle value in a data set when the values are arranged in order. This measure of central tendency is most appropriate when the data set contains extreme values (such as outliers) or when the data is not evenly distributed. In this case, the median value is 18, and it represents the central tendency of the data set better than the mean or mode because both of these measures could be skewed by the two values of 24. The range is not a measure of central tendency, but a measure of dispersion or variability in the data set.

Question 15

Given the following distribution-24,19,15,18,16,24,17-the score that best represents the median is
A) 15
B) 18
C) 19
D) 24

Accepted Answer

To find the median, we first put the scores in order: 15, 16, 17, 18, 19, 24, 24. The median is the score in the middle, which in this case is 18.

Question 16

Patricia wants to report the most common age of the members of her Red Hat group. Which measure should she report?
A) Mode
B) Range
C) Mean
D) Median

Accepted Answer

The answer of Patricia wants to report the most common...

Quiz 12: Descriptive Statistics Activities and Resources

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

Betsy is reporting the results of standardized testing to parents of her class students. Natal received a t score of 80. -Given Natal's t-score, his z-score would be

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.

Which of the following is a measure of variability?

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?

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?

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

Given the following distribution-24,19,15,18,16,24,17-is best described as

Given the following distribution-24,19,15,18,16,24,17-the measure of central tendency best to report is the

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

Patricia wants to report the most common age of the members of her Red Hat group. Which measure should she report?