Z-Scores

What is a Z-Score?

• A measure of the central tendency of a data set.

• A statistical measurement that indicates how many standard deviations an element is from the mean of a data set.

• A method for calculating the variance of a data set.

• A graphical representation of data distribution.

What does it mean if a Z-Score is greater than 2?

• It means the value is more than 2 standard deviations above the mean, indicating it is significantly higher than average.

• It means the value is less than 2 standard deviations below the mean, indicating it is significantly lower than average.

• It means the value is exactly 2 standard deviations above the mean, indicating it is average.

• It means the value is within 2 standard deviations of the mean, indicating it is typical.

Tags

CCSS.HSS.ID.A.4

If the mean is 100 and the standard deviation is 10, what is the Z-Score for 90?

• @@z = rac{{90 - 100}}{{10}} = -1.00@@

• @@z = rac{{90 - 100}}{{5}} = -2.00@@

• @@z = rac{{90 - 100}}{{15}} = -0.67@@

• @@z = rac{{90 - 100}}{{20}} = -0.50@@

What does it mean if a Z-Score is less than -2?

• It means the value is more than 2 standard deviations below the mean, indicating it is significantly lower than average.

• It means the value is exactly at the mean.

• It means the value is more than 2 standard deviations above the mean, indicating it is significantly higher than average.

• It means the value is within 1 standard deviation of the mean.

How do you interpret a Z-Score of 1.5?

• A Z-Score of 1.5 means the value is 1.5 standard deviations above the mean.

• A Z-Score of 1.5 indicates the value is 1.5 units below the mean.

• A Z-Score of 1.5 suggests the value is at the mean level.

• A Z-Score of 1.5 represents a value that is 1.5 times the mean.

If a data set has a mean of 200 and a standard deviation of 25, what is the Z-Score for 250?

• 1.00

• 1.50

• 2.00

• 2.50

What does a positive Z-Score signify?

• A positive Z-Score indicates that the value is above the mean.

• A positive Z-Score indicates that the value is below the mean.

• A positive Z-Score indicates that the value is equal to the mean.

• A positive Z-Score indicates that the value is negative.

What does a negative Z-Score signify?

• A negative Z-Score indicates that the value is below the mean.

• A negative Z-Score indicates that the value is above the mean.

• A negative Z-Score indicates that the value is equal to the mean.

• A negative Z-Score indicates that the value is significantly higher than the mean.

What does a Z-Score of 0 indicate?

• A Z-Score of 0 indicates that the value is exactly equal to the mean.

• A Z-Score of 0 indicates that the value is below the mean.

• A Z-Score of 0 indicates that the value is above the mean.

• A Z-Score of 0 indicates that the value is one standard deviation away from the mean.

How is the Z-Score calculated?

• The Z-Score is calculated using the formula: @@z = rac{{x - ext{mean}}}{{ ext{standard deviation}}}@@ where x is the value, mean is the average of the data set, and standard deviation measures the spread of the data.

• The Z-Score is calculated by taking the average of the data set and dividing it by the total number of values.

• The Z-Score is calculated by subtracting the mean from the value and multiplying by the standard deviation.

• The Z-Score is calculated using the formula: @@z = rac{{ ext{standard deviation}}}{{x - ext{mean}}}@@.