Question 1

If a data set has a mean of 40, what is the sum of the deviations from the mean for all data points?

Accepted Answer

The sum is $$0$$

Question 2

Which pair of measures is resistant to extreme values in a data set?

Accepted Answer

Median and interquartile range (IQR)

Question 3

A population has a larger standard deviation than another measured in the same units. What does this indicate?

Accepted Answer

It has more dispersion

Question 4

According to the Empirical Rule, what percentage of data in a bell-shaped distribution lies within 3 standard deviations of the mean?

Accepted Answer

$$99.7\%$$

Question 5

An observation has a z-score of $$2.3. $$What does this mean?

Accepted Answer

It is $$2.3$$ standard deviations above the mean

Question 6

In a boxplot, the median is left of the center of the box and the right whisker is much longer than the left whisker. What is the shape of the distribution?

Accepted Answer

Skewed right

Question 7

Which tool can you use to describe the percentage of data within $$k$$ standard deviations of the mean when the distribution's shape is unknown?

Accepted Answer

Chebyshev's inequality

Question 8

Which pair of variables would most likely have a negative correlation?

Accepted Answer

Outside temperature and a home's heating bill

Question 9

Which value cannot be a linear correlation coefficient?

Accepted Answer

$$-1.3$$

Question 10

A scatter diagram shows points forming a clear U-shape, and $$r = 0.02. $$Which conclusion is correct?

Accepted Answer

There is no linear relation, but there is a nonlinear relation.

Question 11

For a sample of $$n = 6$$, $$r = -0.92$$ and the critical value is $$0.811. $$What should you conclude?

Accepted Answer

A negative linear relation exists.

Question 12

In a contingency table, what is a marginal distribution?

Accepted Answer

A frequency or relative frequency distribution of either the row or the column variable

Question 13

A coffee shop measures the weights (in grams) of ten shots of espresso: $$8.2, 8.5, 8.5, 8.6, 8.7, 8.8, 9.0, 9.1, 9.2, 9.4. $$What is the sample mean?

Accepted Answer

$$8.8$$ grams

Question 14

Scores on a standardized reading test have a bell-shaped distribution with mean $$75$$ and standard deviation $$5. $$What percentage of scores are between $$70$$ and $$80$$?

Accepted Answer

$$68\%$$

Question 15

Emma finished a 5K race in $$22$$ minutes (mean for women $$26$$, SD $$3). $$Liam finished in $$20$$ minutes (mean for men $$23$$, SD $$2). $$Who performed relatively better?

Accepted Answer

Liam, because his z-score is lower

Question 16

Given the five-number summary $$5, 8, 10, 16, 35$$ for a boxplot, what is the interquartile range (IQR)?

Accepted Answer

$$8$$

Question 17

A small business records monthly advertising spending ($$x$$, in hundreds of dollars) and sales ($$y$$, in thousands of dollars) for five months. The correlation coefficient $$r is$$ $$0.968. $$What does this indicate?

Accepted Answer

There is a strong positive linear association

Question 18

A college surveyed $$200$$ students about their age and class preference. $$120$$ prefer online classes. What proportion of all students prefer online classes, and is this a marginal or conditional proportion?

Accepted Answer

$$0.600$$, marginal

Question 19

If the score $$34 in a $$data set is corrected to $$55$$, what happens to the standard deviation and the interquartile range (IQR)?

Accepted Answer

Standard deviation decreases, IQR is not affected

Question 20

Which of the following statements about correlation and causation is correct?

Accepted Answer

Correlation alone does not establish causation

Step-by-Step Guidance for Statistics Test 2 Practice Problems

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