Percentiles
Marcus is in the 85th percentile for height for boys his age. Interpret this percentile in a complete sentence.
- Marcus is taller than 85% of boys his age.
- Marcus is shorter than 15% of boys his age.
- 15% of boys his age are taller than Marcus.
The mean for your most recent Spanish test is 75 (μ=75) and the standard deviation is 5 (σ=5). If you scored an 85 on the Spanish test, find your z-score.
Recall: z = (x-μ) / σ
z = 2
The mean for a history test is 72 with a standard deviation of 5. Label the normal distribution to help determine what percent of scores are between 67 and 77.
68%
The mean for a history test is 72 with a standard deviation of 5. In what percentile is a student who earned a 77?
84th
Find the range of the data set:
{6, 18, 21, 22, 22, 23, 30}
24
Maria scored in the 42nd percentile on her math test. Which of the following is TRUE?
A. Maria scored a 42% on her math test.
B. 42% of students in Maria's class scored better than she did.
C. 58% of students in Maria's class scored better than she did.
D. Maria's score was 42% higher than the scores of the other students in her class.
C. 58% of students in Maria's class scored better than she did.
The mean for your most recent Spanish test is 75 (μ=75) and the standard deviation is 5 (σ=5). If you scored a 67 on the Spanish test, find your z-score.
Recall: z = (x-μ) / σ
z = -1.6
The mean for a history test is 72 with a standard deviation of 5. Label the normal distribution to help you determine what percent of scores are between 62 and 82.
95%
The mean for a history test is 72 with a standard deviation of 5. In what percentile is a student who earned a 67?
16th
Classify the following variables as either quantitative or categorical:
marital status, place of birth, level of education
categorical
When Arielle was born, she was in the 5th percentile for weight for newborn girls. Which of the following is FALSE?
A. Arielle weighed more than 5% of newborn baby girls.
B. 95% of newborn baby girls weighed more than Arielle.
C. Arielle weighted less than 95% of newborn baby girls.
D. Arielle weighed 5lbs when she was born.
D. Arielle weighed 5lbs when she was born.
You and your best friend are in math class together. On the most recent test, your z-score was -1.3 and your friend's z-score was 1.9. Who scored closer to the mean? Explain your answer.
The mean for a history test is 72 with a standard deviation of 5. Label the normal distribution to help you determine what percent of scores are between 57 and 87.
99.7%
The mean for a history test is 72 with a standard deviation of 5. In what percentile is a student who earned an 82?
- 97.5
- 97th
- 98th
If a data set is skewed right, which of the following should be used to describe the center of the data set?
A) mean
B) median
C) range
D) IQR
B
Your teacher reported percentiles for your most recent Psych test, and you were in the 15th percentile. Are you happy or sad about this result? Explain.
- You are sad because that means 85% of the students in your class scored higher than you did.
- You are sad because that means you scored higher than only 15% of the students in your class.
- You are sad because that means you scored lower than 85% of the students in your class.
The mean for your most recent Science test is 75 (μ=75) and the standard deviation is 3 (σ=3). If you scored an 85 on the Science test, was your score unusual? Explain using z-scores.
Recall: z = (x-μ) / σ
Yes it was unusual because your z-score was 3.33, and any z-score higher than 2 is considered unusual.
The mean for a history test is 72 with a standard deviation of 5. Label the normal distribution to help you determine what percent of scores are above 67.
84%
150 Algebra 2 students took their midterm exam. If Sam is in the 70th percentile, how many students scored lower than Sam?
105
A class of 25 students took a pre-calculus test. If 9 students earned above a B- on the test, what percent of students earned above a B-.
36%