Question 1

Which of the following statements best describes when to use a histogram versus a stem-and-leaf plot?

Accepted Answer

A histogram is more useful for large data sets because it provides a compact display and flexibility in defining intervals.

Question 2

A distribution of annual incomes in a city is highly skewed to the right. Which of the following is most likely true about the mean and median?

Accepted Answer

The mean is greater than the median.

Question 3

Given the data set: 5, 7, 8, 12, 15, 18, 22, what is the median?

Accepted Answer

$$12$$

Question 4

Which of the following is a resistant measure of center?

Accepted Answer

Median

Question 5

A data set has the following values: 2, 4, 4, 4, 5, 7, 9. What is the mode?

Accepted Answer

$$4$$

Question 6

Which of the following best describes the effect of an outlier on the mean and median?

Accepted Answer

The mean is more affected by outliers than the median.

Question 7

A time plot is most appropriate for which type of data?

Accepted Answer

Quantitative data collected over regular intervals of time

Question 8

Given the data set: 3, 7, 7, 10, 12, 15, 18, calculate the range.

Accepted Answer

$$12$$

Question 9

Which of the following statements about the standard deviation $$s is $$true?

Accepted Answer

$$s is $$zero only when all observations are the same.

Question 10

A bell-shaped distribution has a mean of $$50$$ and a standard deviation of $$5. $$According to the Empirical Rule, approximately what percentage of data falls between $$40$$ and $$60$$?

Accepted Answer

About $$68\%$$

Question 11

A data set has the following ordered values: 1, 2, 2, 3, 4, 5, 100. Which value is an outlier, and how does it affect the mean and median?

Accepted Answer

100 is an outlier and increases the mean more than the median.

Question 12

Which of the following best describes a bimodal distribution?

Accepted Answer

A distribution with two distinct peaks.

Question 13

If a distribution is symmetric, which of the following is true?

Accepted Answer

The mean equals the median.

Question 14

A hospital records the number of patients admitted each day for a year. Which graphical method is most appropriate to display trends in this data?

Accepted Answer

Time plot

Question 15

Given the data set: 2, 4, 6, 8, 10, what is the standard deviation? (Round to two decimal places)

Accepted Answer

$$2.83$$

Question 16

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to outliers.

Question 17

A researcher collects the following CO$$_2$$ emission values (in metric tons per person): 0.3, 0.4, 0.8, 1.4, 1.8, 2.1, 5.9, 11.6, 16.9. Which value is an outlier, and why?

Accepted Answer

16.9, because it is much larger than the rest of the data.

Question 18

If a distribution of test scores is skewed to the left, which measure of center is preferred to represent what is typical?

Accepted Answer

Median, because it is resistant to outliers and skewness.

Question 19

A bell-shaped distribution has a mean of $$100$$ and a standard deviation of $$10. $$According to the Empirical Rule, approximately what percentage of data falls between $$80$$ and $$120$$?

Accepted Answer

About $$95\%$$

Question 20

Which of the following best describes the calculation of the sample standard deviation $$s$$ for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\overline{x}$$?

Accepted Answer

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

(Lecture 3) Graphical Representation and Measures of Center and Spread in Statistics

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