MYP Extended Mathematics 8.3 Interpreting Standard Deviation Questionbank

If a height dataset is normally distributed with $\mu = 170\text{ cm}$ and $\sigma = 10\text{ cm}$, about 68% of the heights will be between ________.

When comparing the consistency of two manufacturing processes for producing engine parts, which statistic provides a direct measure of the "predictability" or "typical clustering" of the output size in the original units of measurement (e.g., millimeters)?

3

1

4

2

The data points become more spread out from the mean, and the standard deviation increases.

The data points become more tightly clustered around the mean, and the standard deviation decreases.

The standard deviation remains $10\text{ minutes}$ because the mean commute time of the group has not changed.

The standard deviation increases because the total number of data points has increased.

[50, 58]

[34, 66]

[42, 58]

[46, 54]

160 cm and 180 cm

140 cm and 200 cm

165 cm and 175 cm

150 cm and 190 cm

Variance

Mean

Standard Deviation

Sample Size