Q: A dataset has $$Q_1 = 30$, Q_3$ = 70. $$What is the lower fence for detecting outliers?

$$Q_1 - 1.5$$ \times ($$Q_3$$ - $$Q_1) = 30 - 1.5$$ \times 40 = -30$$

Question 1

Which of the following best describes the difference between a population parameter and a sample statistic?

Accepted Answer

A population parameter is a fixed value that describes a characteristic of the entire population, while a sample statistic is a value calculated from a subset of the population.

Question 2

Given the following data set: 8, 12, 15, 15, 18, 20, 22. What is the median?

Accepted Answer

$$15$$

Question 3

Which measure of center is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 4

A dataset is skewed right. Which measure of center is most appropriate to use?

Accepted Answer

Median

Question 5

Calculate the sample mean for the following data: 4, 10, 12, 12, 13, 21.

Accepted Answer

$$12$$

Question 6

Which formula correctly calculates the sample variance $$s^2$$ for a dataset with $$n$$ values and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 7

A student scored 83% on a chemistry test where the class average was 69% and the standard deviation was 7%. What is the z-score for this student?

Accepted Answer

$$z = \frac{83 - 69}{7} = 2$$

Question 8

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

95%

Question 9

Given a dataset with $$Q_1 = 42$, Q_2$ = 51.5$$, and $$Q_3 = 72.5$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 30.5$$

Question 10

Which of the following is NOT a step in constructing a boxplot?

Accepted Answer

Plot each individual data point as a dot

Question 11

If a dataset is symmetric, which measure of center should you report?

Accepted Answer

Mean

Question 12

Which of the following best describes an outlier?

Accepted Answer

A value that is much higher or lower than most of the other values in the dataset

Question 13

Suppose the mean and standard deviation of a dataset are $$\mu = 50$$ and $$\sigma = 8. $$According to Chebyshev’s Theorem, at least what percentage of data falls within $$k = 2$$ standard deviations of the mean?

Accepted Answer

At least $$75\%$$

Question 14

Which of the following formulas is used to calculate a z-score for a value $$x in a $$dataset with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 15

A dataset has a mean of 20 and a standard deviation of 5. What is the range of values that includes approximately 68% of the data, assuming a bell-shaped distribution?

Accepted Answer

$$15 to$$ $$25$$

Question 16

Which of the following is the correct formula for the sample mean from a frequency distribution, where $$f is $$frequency and $$x is $$the class midpoint?

Accepted Answer

$$\bar{x} = \frac{\sum f \cdot x}{n}$$

Question 17

If the range of a dataset is 20 and the minimum value is 5, what is the maximum value?

Accepted Answer

$$25$$

Question 18

Which of the following statements about standard deviation is TRUE?

Accepted Answer

Standard deviation measures the average distance of data values from the mean.

Question 19

A dataset has $$Q_1 = 30$, Q_3$ = 70. $$What is the lower fence for detecting outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes ($$Q_3$$ - $$Q_1) = 30 - 1.5$$ 	imes 40 = -30$$

Question 20

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the first and third quartiles

Chapter 3: Numerically Summarizing Data – Measures of Center, Spread, and Position

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