Grade 9 Z-Score Practice Worksheet
Practice calculating and interpreting Z-scores on a normal distribution for Grade 9 students.
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Grade 9 Z-Score Practice
Name:
Date:
Score:
Read each question carefully and answer to the best of your ability. Show all your work for calculation questions.
A Z-score (also called a standard score) indicates how many standard deviations an element is from the mean. A positive Z-score means the element is above the mean, while a negative Z-score means it is below the mean. The formula for calculating a Z-score is:
Z = (X - μ) / σ
Where: X = individual data point, μ = mean of the population, σ = standard deviation of the population.
1. What does a Z-score of 0 indicate?
The data point is one standard deviation above the mean.
The data point is equal to the mean.
The data point is one standard deviation below the mean.
The data point is an outlier.
2. If a data set has a mean of 50 and a standard deviation of 10, what is the Z-score for a data point of 65?
-1.5
0.5
1.5
2.5
1. A positive Z-score indicates that the data point is the mean.
2. The standard deviation is a measure of the of data points around the mean.
1. A student scored 85 on a math test. The class average was 70 and the standard deviation was 10. Calculate the student's Z-score.
2. In a certain population, the average height is 160 cm with a standard deviation of 8 cm. What is the Z-score for a person who is 176 cm tall?
Consider a dataset with a mean (μ) of 100 and a standard deviation (σ) of 15.
3. What does a Z-score of -2 mean for a data point in this dataset?
4. If a data point has a Z-score of 1.5, what is its actual value (X)?
1. A Z-score always has a positive value.
True
False
2. A Z-score allows us to compare data points from different normal distributions.
True
False
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