Alg review # 1: measures of center/variation/normal distribution

Front

What is the mean in a data set?

Back

The mean is the average of all the numbers in a data set, calculated by adding all the values and dividing by the number of values.

Front

What does variance measure in a data set?

Back

Variance measures how far a set of numbers are spread out from their average value. It is the average of the squared differences from the mean.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It is the square root of the variance.

Front

What is the first quartile (Q1)?

Back

The first quartile (Q1) is the median of the lower half of a data set, representing the 25th percentile.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

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.

Front

What is the empirical rule in statistics?

Back

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

Front

How do you calculate the interquartile range (IQR)?

Back

The interquartile range (IQR) is calculated by subtracting the first quartile (Q1) from the third quartile (Q3): IQR = Q3 - Q1.

Front

What does a standard deviation of 30 indicate about a data set?

Back

A standard deviation of 30 indicates that the data points tend to be 30 units away from the mean on average, showing a moderate level of dispersion.

Front

If the mean is 75 and the standard deviation is 7, what is the z-score for a score of 82?

Back

The z-score is calculated as (X - mean) / standard deviation. For a score of 82: z = (82 - 75) / 7 = 1.