Q: A frequency distribution is constructed for the prices of GPS navigators. If the minimum price is $$59 and the maximum price is 450$$, and you want 7 classes, what is the correct formula to calculate the class width?

$$\frac{\text{Maximum value} - \text{Minimum value}}{\text{Number of classes}}$$

Q: A weighted mean is calculated using the formula $$\bar{x} = \frac{\sum xw}{\sum w}. If $$your test mean is 86 (weight 0.5), midterm is 96 (weight 0.15), final is 82 (weight 0.2), lab is 98 (weight 0.1), and homework is 100 (weight 0.05), what is your weighted mean?

$$\frac{86 \times 0.5 + 96 \times 0.15 + 82 \times 0.2 + 98 \times 0.1 + 100 \times 0.05}{1} = 88.6$$

Question 1

A frequency distribution is constructed for the prices of GPS navigators. If the minimum price is $$59 and the maximum price is 450$$, and you want 7 classes, what is the correct formula to calculate the class width?

Accepted Answer

$$\frac{	ext{Maximum value} - 	ext{Minimum value}}{	ext{Number of classes}}$$

Question 2

Given the following class limits for a frequency distribution: 59–114, 115–170, 171–226, what are the class boundaries for the first class?

Accepted Answer

$$58.5$$ and $$114.5$$

Question 3

Which type of graph would you use to best display the cumulative frequency of a data set?

Accepted Answer

Ogive

Question 4

A sample of 7 flight prices (in dollars) is: 872, 432, 397, 427, 388, 782, 397. What is the mean price?

Accepted Answer

$$\frac{872 + 432 + 397 + 427 + 388 + 782 + 397}{7} = 527.9$$

Question 5

In a class, the ages of students are: 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 65. Which measure of central tendency is most affected by the outlier?

Accepted Answer

Mean

Question 6

A weighted mean is calculated using the formula $$\bar{x} = \frac{\sum xw}{\sum w}. If $$your test mean is 86 (weight 0.5), midterm is 96 (weight 0.15), final is 82 (weight 0.2), lab is 98 (weight 0.1), and homework is 100 (weight 0.05), what is your weighted mean?

Accepted Answer

$$\frac{86 	imes 0.5 + 96 	imes 0.15 + 82 	imes 0.2 + 98 	imes 0.1 + 100 	imes 0.05}{1} = 88.6$$

Question 7

Which of the following best describes a symmetric distribution?

Accepted Answer

A vertical line can be drawn through the middle and the resulting halves are mirror images.

Question 8

If a data set is skewed right (positively skewed), which of the following is true?

Accepted Answer

The mean is greater than the median.

Question 9

A frequency distribution for the number of minutes spent online is given. The midpoints are 12.5, 24.5, 36.5, 48.5, 60.5, 72.5, 84.5 and the corresponding frequencies are 6, 10, 13, 8, 5, 6, 2. What is the formula to approximate the mean?

Accepted Answer

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

Question 10

Which type of graph is most appropriate for displaying the relationship between two quantitative variables, such as height and weight of students?

Accepted Answer

Scatter plot

Question 11

A dot plot is best used for which type of data?

Accepted Answer

Quantitative data with relatively few distinct values

Question 12

Which of the following is NOT a property of the mode?

Accepted Answer

It is always unique for any data set.

Question 13

A time series chart is most appropriate for which scenario?

Accepted Answer

Tracking the daily temperature over a month

Question 14

If a frequency distribution has classes 10–19, 20–29, 30–39, what is the midpoint of the second class?

Accepted Answer

$$\frac{20 + 29}{2} = 24.5$$

Question 15

Which of the following best describes a uniform distribution?

Accepted Answer

All classes have equal or approximately equal frequencies.

Question 16

A Pareto chart is used to display which type of data?

Accepted Answer

Qualitative data in order of decreasing frequency

Question 17

If a data set has the following frequencies for political party: Democrat (34), Republican (56), Other (21), Did not respond (9), what is the mode?

Accepted Answer

Republican

Question 18

Which of the following is a disadvantage of using the mean as a measure of central tendency?

Accepted Answer

It is greatly affected by outliers.

Question 19

A stem-and-leaf plot is constructed for the number of text messages sent by students. What is a key advantage of this plot compared to a histogram?

Accepted Answer

It retains the original data values.

Descriptive Statistics: Frequency Distributions, Graphs, and Measures of Central Tendency

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