Question 1

George collected achievement score data for each child from a middle school. He has their gender, age, teacher and score on the achievement measure as his data fields.
-George also needs to calculate the measure of variation for achievement score. Which measure should he use?
A) Standard deviation
B) Range
C) Mean
D) Quartile deviation

Accepted Answer

Standard deviation is a measure of dispersion that takes into account the variability of data from the mean. It is a more precise measure of variation than range and quartile deviation. Therefore, it is the best choice for calculating the measure of variation for achievement score.

Question 2

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. What is Claus's approximate t -score?
-Which of the following best represents Claus's z- score?
A) -1.5
B) -.5
C) .5
D) 2.5

Accepted Answer

To find the t-score, we use the formula: t = (raw score - mean) / standard deviation. Plugging in the values, we get: t = (86 - 88) / 4 = -0.5. To find the z-score, we use the formula: z = (raw score - mean) / standard deviation. Plugging in the values, we get: z = (86 - 88) / 4 = -0.5. Therefore, the best choice is B.

Question 3

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions.
-Describe the distribution of the scores.
A) The distribution approximates the normal distribution.
B) the distribution is trimodal.
C) the distribution is negatively skewed.
D) the distribution is positively skewed.

Accepted Answer

The answer of Given the following scores on a midterm...

Question 4

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the median of the distribution is:
A) 78.
B) 86.
C) 90.
D) 98.

Accepted Answer

The median is the middle score when the data is arranged in order from least to greatest. The middle score in this distribution is 90, which is the best choice.

Question 5

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions.
-Calculate the standard deviation of the scores.
A) 4.6
B) 6.8
C) 8.7
D) 9.4

Accepted Answer

The standard deviation is calculated by finding the square root of the variance. The variance is the average of the squared differences from the mean. For these scores, the standard deviation is approximately 8.7.

Question 6

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the range of the distribution is:
A) 10.
B) 12.
C) 16.
D) 20.

Accepted Answer

The range is the difference between the highest and lowest scores in the distribution. The highest score is 98 and the lowest score is 78, so the range is 98-78=20. Therefore, the best choice is D, which represents a range of 20.

Question 7

Logan accessed an existing database to answer his research question regarding the role of identification of a learning disability and odds of going to a private school. The variables of interest include category of disability, type of school, achievement scores in the first, third, and sixth grade, parents SES.
-Logan needs to report the measure of central tendency for his variable category of disability, which measure should he use?
A) Median
B) Mode
C) Mean
D) range

Accepted Answer

For the variable category of disability, mode would be the most appropriate measure of central tendency since it identifies the most common category within the dataset. Median and mean may not be as informative when dealing with categorical data. Range is not a measure of central tendency but rather a measure of dispersion.

Question 8

George collected achievement score data for each child from a middle school. He has their gender, age, teacher and score on the achievement measure as his data fields.
-George needs to calculate the central tendency of his variable achievement score. Which measure should he use?
A) median
B) mode
C) range
D) mean

Accepted Answer

The mean is the best choice for central tendency when dealing with numerical data, as it takes into account all data points and provides a more accurate representation of the average. The median and mode can be affected by outliers and skewness of the data, and the range only provides information about the variability of the data, not its central tendency.

Question 9

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions.
-What is the range?
A) 24
B) 28
C) 32
D) 46

Accepted Answer

The range is calculated by subtracting the smallest score (68) from the largest score (100), which gives 32.

Question 10

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the mode of the distribution is:
A) 80.
B) 86.
C) 92.
D) 98.

Accepted Answer

The mode is the score that appears most frequently in the distribution. In this case, the score of 92 appears twice, making it the mode.

Question 11

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. What is Claus's approximate t -score?
-What is Claus's approximate t score?
A) 0
B) 45
C) 75
D) 90

Accepted Answer

The formula for finding t-score is: 
t = (raw score - mean) / standard deviation
Substituting the values given, 
t = (86 - 88) / 4
t = -0.5
However, since t-score is always positive, we take the absolute value of -0.5 and multiply it by 10 to get an approximate t-score of 5. 
Therefore, the correct answer is B (45).

Question 12

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions.
-What is the median?
A) 88
B) 86
C) 84
D) 82

Accepted Answer

Median is the middle value of a given set of values when assorted in the order from smallest to largest. In this case, the values can be assorted as {68, 72, 74, 76, 78, 80, 84, 86, 87, 88, 89, 90, 90, 91, 92, 93, 94, 94, 96, 100}. Since there are even number of values in the set, the median is the average of two middle values. Therefore, the median is (88+89)/2 = 88.5, which is rounded to 88.

Question 13

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions.
-What is the mode?
A) 68
B) 76
C) 84
D) 90

Accepted Answer

The mode is the score that appears the most frequently in the dataset. In this case, the score of 90 appears three times, which is more than any other score. Therefore, the mode is 90.

There is no question asking for the "best choice(s)" with an explanation, so this is an invalid question.

Question 14

Logan accessed an existing database to answer his research question regarding the role of identification of a learning disability and odds of going to a private school. The variables of interest include category of disability, type of school, achievement scores in the first, third, and sixth grade, parents SES.
-Logan will report a measure of variability for each of the achievement scores. Which will he most likely report?
A) Mean
B) Range
C) Standard Deviation
D) Median

Accepted Answer

Standard deviation is a measure of variability that describes how much the scores in a distribution differ from the mean. It is commonly used to report the dispersion of scores around the central tendency (i.e., mean). Thus, Logan will most likely report standard deviation for each of the achievement scores. This will give a sense of how much the students' performance varied from the mean in each grade level.

Question 15

Logan accessed an existing database to answer his research question regarding the role of identification of a learning disability and odds of going to a private school. The variables of interest include category of disability, type of school, achievement scores in the first, third, and sixth grade, parents SES.
-Logan needs to report the correlations among first, third, and sixth grade achievement scores. Which is the most likely measure of relationship appropriate for him to use?
A) Spearman Rho
B) Pearson r
C) Cronbach's alpha
D) Kendall's Tau

Accepted Answer

Pearson r is the most appropriate measure of correlation for variables that have a linear relationship, such as achievement scores across different grades. The other options, Spearman Rho, Cronbach's alpha, and Kendall's Tau, are not appropriate for measuring linear correlations among continuous variables.

Question 16

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions.
-Calculate the mean of the scores.
A) 83
B) 86
C) 90
D) 92

Accepted Answer

To find the mean, we sum up all the scores and divide by the total number of scores.

Sum of scores = 72+89+91+90+100+68+80+76+78+94+94+90+84+86+88+87+92+96+74+93 = 1718

Total number of scores = 20

Mean = Sum of scores / Total number of scores = 1718 / 20 = 85.9, which rounds up to 86.

Therefore, the correct choice is B.

Question 17

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. What is Claus's approximate t -score?
-What can we conclude about Claus's stanine score?
A) It is negative.
B) It is approximately zero.
C) It is approximately 5.
D) It is approximately 8.

Accepted Answer

Claus's t-score is approximately 5 because his raw score is 2 points below the mean, and the standard deviation is 4. A t-score of 5 means that Claus performed better than about 99% of the other test takers. His stanine score would be 9, which is the highest possible score.

Question 18

Cynthia is reporting standardized test scores to parents of her students. She knows that on the test she gave the mean is an 80 and the standard deviation is 6. If her student Sharona received a t score of 40, which of the following can we accurately conclude regarding Sharona's performance?
A) She had a raw score greater than 80.
B) She had a positive z -score.
C) Her stanine score was an 8.
D) Her performance was less than average.

Accepted Answer

A t score of 40 is below the mean of 50 for t scores, indicating that Sharona's performance was less than average. Raw scores cannot be determined from t scores, and stanine scores are not related to t scores. It is also not possible to determine whether Sharona's z-score was positive or negative without additional information.

Question 19

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?
A) Range
B) Standard deviation
C) Median
D) Mean

Accepted Answer

The median is the middle value in a data set, so it is not influenced by extreme outliers like two students with much lower scores. The mean (D) could be heavily influenced by those outliers, and the range (A) and standard deviation (B) do not give a measure of central tendency.

Question 20

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the mean of the distribution is:
A) 84.
B) 89.
C) 93.
D) 98.

Accepted Answer

To find the mean, we add up all the scores and divide by the total number of scores. (88+90+78+82+94+86+80+92+92+96+98)/11 = 89. Therefore, B) 89 is the score that best represents the mean of the distribution.

Quiz 12: Descriptive Statistics Activities and Resources

George collected achievement score data for each child from a middle school. He has their gender, age, teacher and score on the achievement measure as his data fields. -George also needs to calculate the measure of variation for achievement score. Which measure should he use?

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. What is Claus's approximate t -score? -Which of the following best represents Claus's z- score?

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions. -Describe the distribution of the scores.

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the median of the distribution is:

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions. -Calculate the standard deviation of the scores.

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the range of the distribution is:

George collected achievement score data for each child from a middle school. He has their gender, age, teacher and score on the achievement measure as his data fields. -George needs to calculate the central tendency of his variable achievement score. Which measure should he use?

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions. -What is the range?

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the mode of the distribution is:

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. What is Claus's approximate t -score? -What is Claus's approximate t score?

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions. -What is the median?

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions. -What is the mode?

Given the following scores on a midterm exam 72, 89, 91, 90, 100, 68, 80,76, 78,94,94,90,84,86,88,87,92,96,74,93, find the best answer to the following questions. -Calculate the mean of the scores.

Claus received a raw score of 86. Given that the test had a mean of 88, and a standard deviation of 4. What is Claus's approximate t -score? -What can we conclude about Claus's stanine score?

Cynthia is reporting standardized test scores to parents of her students. She knows that on the test she gave the mean is an 80 and the standard deviation is 6. If her student Sharona received a t score of 40, which of the following can we accurately conclude regarding Sharona's performance?

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?

Given the following distribution of test scores: 88,90,78,82,94,86,80,92,92,96,98. The score that best represents the mean of the distribution is: