Question

1. choose the best answer.

which statement is true?
the size of standard deviation does not affect the variation of the data set.
the greater the standard deviation, the lower the variation.
the greater the standard deviation, the greater the variation.

1. choose the best answer.

which statement is true?
the greater the variation, the less the reliability of the mean.
the greater the variation, the greater the reliability of the mean.
variability does not affect the reliability of the data set.

1. choose the best answer.

which statement is true?
approximately 68.2% of the values are within 1 standard deviation (above or below) from the mean.
approximately 68.2% of the values are at 3 standard deviations (above or below) from the mean.
approximately 68.2% of the values are at 2 standard deviations (above or below) from the mean.

1. choose the best answer.

Explanation:

Question 4

Standard deviation measures data variation. A larger standard deviation means data points are more spread out (greater variation), a smaller one means less spread (lower variation). The first option is wrong (standard deviation affects variation), the second is wrong (greater SD means greater, not lower, variation). The third option correctly states the relationship.

Variation (dispersion) impacts mean reliability. Higher variation means data is more spread, so the mean is less representative (less reliable). The second option is wrong (greater variation reduces reliability), the third is wrong (variability does affect reliability). The first option is correct.

By the empirical rule (for normal distributions), ~68.2% of data lies within 1 standard deviation of the mean, ~95.4% within 2, ~99.7% within 3. The second option is wrong (3 SD has ~99.7%), the third is wrong (2 SD has ~95.4%). The first option is correct.

Answer:

The greater the standard deviation, the greater the variation.

Question 5