Question 1

Which of the following best describes the 'range' in a data set?

Accepted Answer

The difference between the maximum value and the minimum value.

Question 2

Given the data set: 1, 3, 3, 1.5, 1, 6, what is the range?

Accepted Answer

$$6 - 1 = 5$$

Question 3

Which statement about the standard deviation is TRUE?

Accepted Answer

It measures how much the data values differ from the mean.

Question 4

What is the formula for the sample standard deviation $$s$$?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 5

For the data set 1, 3, 3, 1.5, 1, 6, what is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = 2.75$$

Question 6

Which of the following is a property of the standard deviation?

Accepted Answer

It is greatly affected by extreme values.

Question 7

If all values in a data set are the same, what is the standard deviation?

Accepted Answer

It is zero.

Question 8

Which formula is used to calculate the population standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}$$

Question 9

Why is the sample standard deviation $$s$$ considered a biased estimator of the population standard deviation $$\sigma$$?

Accepted Answer

Because it divides by $$n$$ instead of $$n-1.$$

Question 10

What is the variance of a data set?

Accepted Answer

The average of the squared deviations from the mean.

Question 11

Which of the following statements about variance is FALSE?

Accepted Answer

Variance is measured in the same units as the original data.

Question 12

A medical researcher collects the following cholesterol levels (mg/dL) from six patients: 180, 190, 185, 200, 195, 210. What is the range?

Accepted Answer

$$210 - 180 = 30$$

Question 13

Using the 'Range Rule of Thumb', estimate the standard deviation for the data set: 1, 3, 3, 1.5, 1, 6.

Accepted Answer

$$\frac{5}{4} = 1.25$$

Question 14

Which scenario would likely result in a higher standard deviation?

Accepted Answer

A group of students with test scores spread widely from the mean.

Question 15

Why does the sample standard deviation use $$n-1 in $$the denominator instead of $$n$$?

Accepted Answer

To correct for bias in estimating the population variance.

Question 16

A biologist measures the weights of 7 rocks: 2, 4, 4, 5, 6, 8, 10 grams. What is the sample standard deviation? (Round to two decimal places)

Accepted Answer

$$2.67$$

Question 17

Which of the following is NOT a measure of variation?

Accepted Answer

Mean

Question 18

If the range of a data set is 12 and the estimated standard deviation using the Range Rule of Thumb is 3, what is the formula used?

Accepted Answer

$$	ext{Estimated standard deviation} = \frac{	ext{Range}}{4}$$

Question 19

A teacher records the following test scores: 70, 75, 80, 85, 90. What is the variance of the scores?

Accepted Answer

$$50$$

Measures of Variation in Statistics: Range, Standard Deviation, and Variance

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