Z Scores
A data value is 14, the mean is 10, and the standard deviation is 2. This is the z-score.
What is 2?
A data set has 20 values. Find the position c of the 40th percentile.
What is 8?
A data set has 20 values. Using the formula this is the position of the first quartile (Q1).
What is 5?
For a data set, Q1 = 10 and Q3 = 18. This is the interquartile range (IQR).
What is 8?
In a five-number summary, this value represents the middle of the data set.
What is the median?
A student scored 72 on a quiz where the mean is 80 and the standard deviation is 4. This is the z-score.
What is –2?
In a class of 30 students, 18 students scored below Alex, and 0.5 is added per the formula. This is Alex’s percentile rank.
What is the 62nd percentile?
In a set of 32 data values, find the position of the third quartile (Q3).
What is 24?
Q1 = 12 and Q3 = 20. Using the IQR method, calculate the lower fence.
What is 0?
The ordered data set is:
4, 7, 9, 10, 12, 13, 15, 18
This value is Q1.
What is 9?
A distribution has mean 50 and standard deviation 5. A student’s z-score is 1.6. This is the student’s actual score.
What is 58?
You want the 75th percentile of a data set with 16 values. This is the position number c.
What is 12?
A data set has 25 values. Find the position of Decile 4 (40th percentile).
What is 10?
Q1 = 25, Q3 = 40. A data point is 65. Determine if it is an outlier.
What is “Yes, it is an outlier”?
The left whisker of a boxplot touches 20 and the right whisker touches 92. These are the minimum and maximum values.
What are 20 (min) and 92 (max)?
A student’s score is 92, and the standard deviation is 6. If the student’s z-score is 1.5, this is the mean of the distribution.
What is 83?
Maria is at the 80th percentile in a group of 25 students. Using the percentile rank formula, this is how many students scored below her.
What is 19.5 students, meaning she falls between the 19th and 20th student?
A student’s score is located at the position where 14 values are below it in a data set of 40. This is the student’s percentile rank and tells whether they are above Q1, Q2, Q3, or Q4.
What is the 37% percentile, which falls below Q2?
Q1 = 30, Q3 = 50. A value in the data set is 5. Using the IQR method, determine whether it is an outlier.
What is “No, 5 is not an outlier”?
Group A has Q1 = 15 and Q3 = 30
Group B has Q1 = 22 and Q3 = 35
This group has the larger interquartile range.
What is Group A?
(IQR A = 15, IQR B = 13)
A data point of 130 has a z-score of –0.75 in a distribution with mean 140. This is the standard deviation.
What is 13.33?
In a data set of 48 values, a student has 31 values below theirs. This is the student’s percentile rank.
Answer: What is 66th percentile?
In a data set of 60 values, a student’s score has 47 values below it. Using the percentile rank formula, determine the student’s percentile and which decile they fall into.
What is the 79% percentile, which places them in the 8th decile?
Q1 = 14 and Q3 = 29. Data values include 45 and –2. Determine which, if any, are outliers.
What is “Neither value is an outlier”?
You compare two boxplots representing test scores.
Group X: median = 72, Q1 = 68, Q3 = 90
Group Y: median = 80, Q1 = 70, Q3 = 85
This group has the higher overall center, but this group has the more spread-out middle 50%.
What is: Group Y has the higher center (median 80), and Group X has the larger IQR (90–68 = 22)?