Alg IIb - Obj 81 Mean and standard deviation

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What is the mean in a data set?

Back

The mean is the average of all data points, calculated by summing all values and dividing by the number of values.

Tags

CCSS.6.SP.B.5C

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What is standard deviation?

Back

Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

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What does the empirical rule state about data in a normal distribution?

Back

The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the normal range (68%) for a given mean and standard deviation?

Back

The normal range (68%) can be calculated by taking the mean and subtracting and adding one standard deviation. For example, if the mean is 29 and the standard deviation is 3, the range is 29-3 to 29+3, which is 26 to 32.

Tags

CCSS.HSS.ID.A.4

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Back

Front

What is the significance of the shaded area in a normal distribution graph?

Back

The shaded area in a normal distribution graph typically represents the proportion of data that falls within a certain range of values, often related to standard deviations from the mean.

Tags

CCSS.HSS.ID.A.4

Front

If a data set has a mean of 50 and a standard deviation of 10, what is the range of values that fall within one standard deviation?

Back

The range of values that fall within one standard deviation is from 40 to 60 (50 - 10 to 50 + 10).

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

Tags

CCSS.HSS.ID.A.4

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What is the formula for calculating standard deviation?

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What is the difference between population standard deviation and sample standard deviation?

Back

Population standard deviation is calculated using all members of a population, while sample standard deviation is calculated using a subset of the population and includes a correction factor (N-1) in the denominator.