Review of Variation and Position

Front

What is the Empirical Rule in statistics?

Back

The Empirical Rule states that for a normal distribution, 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.

Front

What does the standard deviation represent in a data set?

Back

The 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.

Front

Calculate the mean of the following data set: 63, 71, 65, 66, 87, 53.

Back

Mean = (63 + 71 + 65 + 66 + 87 + 53) / 6 = 67.5.

Front

What is the formula for calculating the range of a data set?

Back

Range = Maximum value - Minimum value.

Front

If the mean life of a tire is 30,000 km and the standard deviation is 2000 km, what is the range for 68% of the tires?

Back

28,000 km to 32,000 km.

Front

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

Back

Approximately 95%.

Front

What is the symbol for the mean in statistics?

Back

The symbol for the mean is μ.

Front

How do you find the standard deviation of a data set?

Back

1. Calculate the mean. 2. Subtract the mean from each data point and square the result. 3. Find the average of these squared differences. 4. Take the square root of that average.

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the significance of the 68-95-99.7 rule?

Back

It describes the percentage of data that falls within one, two, and three standard deviations from the mean in a normal distribution.