Question 1

If Joe scored 25 on a test with a mean of 20 and a standard deviation of 5 what is his z-score?​
A)25
B)+1.0
C)0.0
D)cannot be determined

Accepted Answer

To find the z-score, we use the formula:
z = (x - µ) / σ
where x is the individual score, µ is the population mean, and σ is the population standard deviation.

In this case, Joe's score is x = 25, the population mean is µ = 20, and the population standard deviation is σ = 5.

Substituting these values, we get:
z = (25 - 20) / 5
z = 1.0

Therefore, Joe's z-score is +1.0.

Question 2

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consumes an amount between 4 and 6 cups?​
A)0.5468
B)0.4972
C)0.50
D)none of the options is correct

Accepted Answer

To solve this problem, we need to standardize the values using the formula:

z = (X - µ) / σ

where X is the value we want to find the proportion for (in this case, between 4 and 6 cups), µ is the mean (5 cups), and σ is the standard deviation (1.5 cups).

z1 = (4 - 5) / 1.5 = -0.67

z2 = (6 - 5) / 1.5 = 0.67

Now we look up the proportion of values between -0.67 and 0.67 in a standard normal distribution table, which is 0.4972.

Therefore, the proportion of faculty who consume an amount between 4 and 6 cups is 0.4972 or approximately 0.50. The answer is B.

Question 3

Draw the frequency polygon for the following distribution (there are 30 scores in the distribution). In addition, calculate the mean, median, and mode for the distribution.
48, 50, 53, 59, 59, 63, 63, 67, 67, 67, 72, 72, 72, 78, 78, 78, 78, 85, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 98, 100
​

Accepted Answer

The answer of Draw the frequency polygon for the following...

Question 4

Explain the difference in proper use between a bar graph and a histogram.

Accepted Answer

The answer of Explain the difference in proper use between...

Question 5

A z-score is most affected by the​
A)median.
B)mode.
C)standard deviation.
D)range.

Accepted Answer

A z-score measures the number of standard deviations a data point is from the mean. Therefore, the most important factor for calculating a z-score is the standard deviation, as it is used to calculate the number of standard deviations a data point is away from the mean. The median, mode, and range do not factor into the calculation of a z-score.

Question 6

The calculation of the average deviation differs from the calculation of the standard deviation in that when calculating the average deviation the difference scores are​
A)squared.
B)converted to absolute values.
C)squared and converted to absolute values.
D)it does not differ.

Accepted Answer

When calculating the average deviation, the difference scores are simply converted to absolute values by taking the absolute value of each difference and then averaging them. In contrast, when calculating the standard deviation, the difference scores are squared, summed, divided by the sample size minus one, and then the square root is taken of that result.

Question 7

Explain the difference between qualitative and quantitative variables noting the relationship of nominal, ordinal, interval, and ratio data to these terms.​

Accepted Answer

The answer of Explain the difference between qualitative and quantitative...

Question 8

Which of the following is FALSE?​
A)The range is a simplistic measure of variation that does not use all scores in the distribution in its calculation.
B)The average deviation is a more sophisticated measure of variation than the range in which all scores are used but which may not weight extreme scores adequately.
C)The standard deviation is the least sophisticated measure of variation and the least frequently used.
D)all of the options are true

Accepted Answer

The standard deviation is actually one of the most commonly used measures of variation and is considered to be a more sophisticated measure than the range or average deviation as it uses all scores in the distribution and gives greater weight to extreme scores. Therefore, option C is false.

Question 9

Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _____ standard deviation and a _____ average deviation in comparison to distribution B.​
A)larger; larger
B)smaller; smaller
C)larger; smaller
D)smaller; larger

Accepted Answer

The answer of Imagine that distribution A contains the following...

Question 10

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What is the percentile rank for an individual who consumed 8 cups of coffee per day?​
A)97.72
B)2.28
C)47.72
D)none of the options is correct

Accepted Answer

To find the percentile rank, we need to calculate the z-score for someone who consumed 8 cups of coffee:

z = (x - μ) / σ
z = (8 - 5) / 1.5
z = 2

Using a z-table or calculator, we can find that the area to the left of z = 2 is approximately 0.9772. This means that 97.72% of the faculty in the psychology department consume fewer than 8 cups of coffee per day. To find the percentile rank for someone who consumed 8 cups of coffee, we need to subtract this value from 1:

Percentile rank = 1 - 0.9772 = 0.0228
Percentile rank = 2.28

Therefore, the answer is A) 97.72.

Question 11

Approximately what percentage of scores are between z=1 and z=2?​
A)50
B)68
C)16
D)13.5

Accepted Answer

The answer of Approximately what percentage of scores are between...

Question 12

Karen's first psychology exam score is ‑1 standard deviation from the mean in a normal distribution. The test has a mean of 75 and a standard deviation of 5. Karen's percentile rank would be​
A)16%.​
B)54%.
C)70%.
D)cannot determine from the information given

Accepted Answer

The answer of Karen's first psychology exam score is ‑1...

Question 13

Which of the following is a disadvantage of using the range as a measure of variation?​
A)It is limited because only two of the scores in the distribution are used to derive it.
B)It is easily distorted by an unusually high or low score in a distribution.
C)It can only be used with nominal data.
D)It is limited because only two of the scores in the distribution are used to derive it, and it is easily distorted by an unusually high or low score in a distribution.

Accepted Answer

Choice D is correct because it accurately identifies both limitations of using the range as a measure of variation. Only considering the two extreme scores in a distribution can be misleading, especially if there are outliers that significantly impact the range. Additionally, the range can be distorted by a single unusually high or low score in the distribution, which may not be representative of the rest of the data. Choices A, B, and C all describe limitations or issues with the range, but only D includes both major drawbacks.

Question 14

If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, then approximately 95% of all women should be between _____ and _____ inches in height.​
A)62.5; 67.7
B)60; 70
C)57.5; 72.5
D)cannot determine from the information given

Accepted Answer

The answer of If the average height for women is...

Question 15

If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the right than to the left, how would the distribution be skewed?​
A)normally​
B)negatively
C)positively
D)average

Accepted Answer

A long tail projecting longer to the right than to the left indicates a positive skew, as the mean would be pulled towards the right by the extreme values.

Question 16

Sue took a test in both biology and math last week. The biology test had a mean of 70 and a standard deviation of 7 whereas the math test had a mean of 75 and a standard deviation of 10. Sue scored a 76 on the biology test and a 76 on the math test. On which test did she do better in comparison to the rest of the class?​
A)the math test
B)the biology test
C)she did the same on each test
D)cannot be determined

Accepted Answer

We can use z-scores to compare Sue's scores to the rest of the class. The formula for calculating a z-score is:

z = (x - μ) / σ

where:
x = Sue's score
μ = mean of the class
σ = standard deviation of the class

For the biology test:

z = (76 - 70) / 7 = 0.86

For the math test:

z = (76 - 75) / 10 = 0.1

A positive z-score means that Sue scored above the class average, while a negative z-score means she scored below the class average.

Since Sue's z-score is higher for the biology test (0.86) than for the math test (0.1), she did better in comparison to the rest of the class on the biology test. Therefore, the best choice is B, the biology test.

Question 17

Rich's first psychology exam score is +1 standard deviation from the mean in a normal distribution. The test has a mean of 60 and a standard deviation of 6. Rich's percentile rank would be approximately​
A)70%.
B)84%.
C)66%.
D)cannot determine from the information given

Accepted Answer

Using the formula for z-score, which is (x-μ)/σ, we can calculate Rich's z-score as (x-60)/6 = 1, where x is Rich's score. Solving for x, we get x = 66. Therefore, Rich's score is 1 standard deviation above the mean, which corresponds to the 84th percentile in a normal distribution. Thus, the answer is B.

Question 18

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. How many cups of coffee would an individual at the 25th percentile drink per day?​
A)4
B)5
C)6
D)7

Accepted Answer

The 25th percentile corresponds to a z-score of approximately -0.675. Using the formula X = μ + Zσ, where μ = 5 and σ = 1.5, we calculate X = 5 + (-0.675)(1.5) = 4.9875, which rounds to 4 cups.

Question 19

In a psychology class of 100 students, test scores are normally distributed with a mean of 80 and a standard deviation of 5. Approximately what percentage of students have scores between 70 and 90?​
A)68%
B)80%
C)95%
D)99%

Accepted Answer

We can use the empirical rule to estimate the percentage of students with scores between 70 and 90. According to the empirical rule, approximately 68% of the scores should fall within one standard deviation of the mean (i.e., between 75 and 85), approximately 95% should fall within two standard deviations of the mean (i.e., between 70 and 90), and approximately 99% should fall within three standard deviations of the mean (i.e., between 65 and 95).

Since we are interested in the percentage of students with scores between 70 and 90, which falls within two standard deviations of the mean, we can estimate that approximately 95% of the students have scores in this range. Therefore, the best choice is C.

Question 20

Calculate the mean, median, and mode for the following sample: 2, 2, 6, 9, 10, 11, 15, 17, 18, 20.​

Accepted Answer

The answer of Calculate the mean, median, and mode for...

Quiz 5: Data Organization and Descriptive Statistics

If Joe scored 25 on a test with a mean of 20 and a standard deviation of 5 what is his z-score?

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consumes an amount between 4 and 6 cups?

Draw the frequency polygon for the following distribution (there are 30 scores in the distribution). In addition, calculate the mean, median, and mode for the distribution. 48, 50, 53, 59, 59, 63, 63, 67, 67, 67, 72, 72, 72, 78, 78, 78, 78, 85, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 98, 100

Explain the difference in proper use between a bar graph and a histogram.

A z-score is most affected by the

The calculation of the average deviation differs from the calculation of the standard deviation in that when calculating the average deviation the difference scores are

Explain the difference between qualitative and quantitative variables noting the relationship of nominal, ordinal, interval, and ratio data to these terms.

Which of the following is FALSE?

Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _ standard deviation and a _ average deviation in comparison to distribution B.

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What is the percentile rank for an individual who consumed 8 cups of coffee per day?

Approximately what percentage of scores are between z=1 and z=2?

Karen's first psychology exam score is ‑1 standard deviation from the mean in a normal distribution. The test has a mean of 75 and a standard deviation of 5. Karen's percentile rank would be

Which of the following is a disadvantage of using the range as a measure of variation?

If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, then approximately 95% of all women should be between _ and _ inches in height.

If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the right than to the left, how would the distribution be skewed?

Rich's first psychology exam score is +1 standard deviation from the mean in a normal distribution. The test has a mean of 60 and a standard deviation of 6. Rich's percentile rank would be approximately

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. How many cups of coffee would an individual at the 25th percentile drink per day?

In a psychology class of 100 students, test scores are normally distributed with a mean of 80 and a standard deviation of 5. Approximately what percentage of students have scores between 70 and 90?

Calculate the mean, median, and mode for the following sample: 2, 2, 6, 9, 10, 11, 15, 17, 18, 20.

Quiz 5: Data Organization and Descriptive Statistics

If Joe scored 25 on a test with a mean of 20 and a standard deviation of 5 what is his z-score?​

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consumes an amount between 4 and 6 cups?​

Draw the frequency polygon for the following distribution (there are 30 scores in the distribution). In addition, calculate the mean, median, and mode for the distribution. 48, 50, 53, 59, 59, 63, 63, 67, 67, 67, 72, 72, 72, 78, 78, 78, 78, 85, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 98, 100 ​

Explain the difference in proper use between a bar graph and a histogram.

A z-score is most affected by the​

The calculation of the average deviation differs from the calculation of the standard deviation in that when calculating the average deviation the difference scores are​

Explain the difference between qualitative and quantitative variables noting the relationship of nominal, ordinal, interval, and ratio data to these terms.​

Which of the following is FALSE?​

Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _____ standard deviation and a _____ average deviation in comparison to distribution B.​

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What is the percentile rank for an individual who consumed 8 cups of coffee per day?​

Approximately what percentage of scores are between z=1 and z=2?​

Karen's first psychology exam score is ‑1 standard deviation from the mean in a normal distribution. The test has a mean of 75 and a standard deviation of 5. Karen's percentile rank would be​

Which of the following is a disadvantage of using the range as a measure of variation?​

If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, then approximately 95% of all women should be between _____ and _____ inches in height.​

If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the right than to the left, how would the distribution be skewed?​

Rich's first psychology exam score is +1 standard deviation from the mean in a normal distribution. The test has a mean of 60 and a standard deviation of 6. Rich's percentile rank would be approximately​

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. How many cups of coffee would an individual at the 25th percentile drink per day?​

In a psychology class of 100 students, test scores are normally distributed with a mean of 80 and a standard deviation of 5. Approximately what percentage of students have scores between 70 and 90?​

Calculate the mean, median, and mode for the following sample: 2, 2, 6, 9, 10, 11, 15, 17, 18, 20.​

If Joe scored 25 on a test with a mean of 20 and a standard deviation of 5 what is his z-score?

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consumes an amount between 4 and 6 cups?

Draw the frequency polygon for the following distribution (there are 30 scores in the distribution). In addition, calculate the mean, median, and mode for the distribution. 48, 50, 53, 59, 59, 63, 63, 67, 67, 67, 72, 72, 72, 78, 78, 78, 78, 85, 85, 85, 85, 85, 90, 90, 90, 90, 95, 95, 98, 100

A z-score is most affected by the

The calculation of the average deviation differs from the calculation of the standard deviation in that when calculating the average deviation the difference scores are

Explain the difference between qualitative and quantitative variables noting the relationship of nominal, ordinal, interval, and ratio data to these terms.

Which of the following is FALSE?

Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _ standard deviation and a _ average deviation in comparison to distribution B.

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What is the percentile rank for an individual who consumed 8 cups of coffee per day?

Approximately what percentage of scores are between z=1 and z=2?

Karen's first psychology exam score is ‑1 standard deviation from the mean in a normal distribution. The test has a mean of 75 and a standard deviation of 5. Karen's percentile rank would be

Which of the following is a disadvantage of using the range as a measure of variation?

If the average height for women is normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, then approximately 95% of all women should be between _ and _ inches in height.

If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the right than to the left, how would the distribution be skewed?

Rich's first psychology exam score is +1 standard deviation from the mean in a normal distribution. The test has a mean of 60 and a standard deviation of 6. Rich's percentile rank would be approximately

Faculty in the psychology department at State University consume an average of 5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. How many cups of coffee would an individual at the 25th percentile drink per day?

In a psychology class of 100 students, test scores are normally distributed with a mean of 80 and a standard deviation of 5. Approximately what percentage of students have scores between 70 and 90?

Calculate the mean, median, and mode for the following sample: 2, 2, 6, 9, 10, 11, 15, 17, 18, 20.