Question 1

Which of the following is NOT a measure of center discussed in statistics?

Accepted Answer

Standard deviation

Question 2

Given the data set: 70, 44, 12, 23, 46, 7, 47, 31, 35, 54, 73, what is the mean of the jersey numbers?

Accepted Answer

$$\frac{442}{11} = 40.18$$

Question 3

Standard deviation describes:

Accepted Answer

The spread of data values around the mean

Question 4

If the standard deviation of a dataset is $$100$$ dollars, what is the variance?

Accepted Answer

$$100^2 = 10$$,000$$ dollars squared

Question 5

For any dataset, at least what percentage of values are within 2 standard deviations of the mean according to Chebyshev's theorem?

Accepted Answer

75%

Question 6

For a normally distributed set, what percentage of values are expected within 2 standard deviations of the mean?

Accepted Answer

95%

Question 7

A value is considered significantly high if it is at least how many standard deviations above the mean?

Accepted Answer

2

Question 8

According to the Empirical Rule, what percentage of values in a normal distribution are within one standard deviation of the mean?

Accepted Answer

68%

Question 9

Chebyshev’s theorem states that the proportion of any set of data lying within $$k$$ standard deviations is always at least:

Accepted Answer

$$1 - \frac{1}{k^2$}$$

Question 10

Use Chebyshev’s theorem for $$k = 3. $$What proportion of the data lies within 3 standard deviations of the mean?

Accepted Answer

$$1 - \frac{1}{9} = \frac{8}{9} \approx 88.9\%$$

Question 11

Which of the following is NOT a measure of variation?

Accepted Answer

Median

Question 12

If the variance of a sample is $$25$$, what is the standard deviation?

Accepted Answer

$$\sqrt{25} = 5$$

Question 13

If you want to know how many standard deviations from the mean your value is, which formula should you use?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 14

A basketball player’s height is 198 cm, and his z score is 3.38. How many standard deviations above the mean is his height?

Accepted Answer

3.38

Question 15

Which z score would you prefer for your statistics test result: -2.00, -1.00, 0, 1.00, or 2.00? Why?

Accepted Answer

2.00, because it means your score is 2 standard deviations above the mean

Question 16

Which of the following is a measure of position?

Accepted Answer

Quartile

Question 17

The value that is greater than or equal to 50% of your values and less than or equal to the other 50% is called:

Accepted Answer

Median

Question 18

If the minimum value in a dataset is 5, what does this tell you about the other values?

Accepted Answer

All values are greater than or equal to 5

Question 19

Given the hurricane data: 3, 5, 2, 4, 6, 3, 7, 2, 5, 4, what is the range?

Accepted Answer

$$7 - 2 = 5$$

Question 20

Which important feature of the hurricane data is NOT revealed by any of the measures of variation?

Accepted Answer

The pattern or trend over time

Introductory Statistics: Measures of Center, Variation, and Position

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