Q: In a frequency distribution, how is the class midpoint calculated?

Class midpoint = $$\frac{\text{lower class limit} + \text{upper class limit}}{2}$$

Q: A pie chart is used to show the proportion of responses in each category. If a category has a frequency $$f$$ and the total number of responses is $$n$$, what is the formula for the relative frequency percentage?

Relative frequency (%) = $$\frac{f}{n} \times 100\%$$

Question 1

Which of the following best describes the difference between qualitative and quantitative data?

Accepted Answer

Qualitative data consists of names or labels, while quantitative data consists of numerical values.

Question 2

A frequency distribution table is constructed to show the frequency of observations across different classes. If the minimum value in a data set is 16 and the maximum value is 71, and you want to organize the data into 7 classes, what is the class width?

Accepted Answer

Class width = $$\frac{71-16}{7}$$, rounded up to the nearest whole number

Question 3

Which type of graph is most appropriate for displaying the frequency of categorical (qualitative) data?

Accepted Answer

Bar Chart

Question 4

In a frequency distribution, how is the class midpoint calculated?

Accepted Answer

Class midpoint = $$\frac{	ext{lower class limit} + 	ext{upper class limit}}{2}$$

Question 5

A pie chart is used to show the proportion of responses in each category. If a category has a frequency $$f$$ and the total number of responses is $$n$$, what is the formula for the relative frequency percentage?

Accepted Answer

Relative frequency (%) = $$\frac{f}{n} 	imes 100\%$$

Question 6

Which of the following best describes a Pareto chart?

Accepted Answer

A bar graph where bars are arranged in descending order of frequency.

Question 7

A histogram is constructed for a data set. Which axis should display the class midpoints?

Accepted Answer

Horizontal axis

Question 8

If a frequency distribution has classes 5–15, 16–26, 27–37, 38–48, 49–59, 60–70, and 71–81, what is the class width?

Accepted Answer

Class width = $$16 - 5 = 11$$

Question 9

Which of the following best describes a frequency polygon?

Accepted Answer

A graph that uses points connected by segments to show frequencies across class midpoints.

Question 10

A stemplot displays quantitative data by showing both the stem and leaf of each value. If a stemplot contains the row 2|0024555789, which data points are represented?

Accepted Answer

20, 20, 24, 25, 25, 57, 58, 59

Question 11

Which type of graph is most appropriate for showing trends in data over time, such as monthly sales or daily temperatures?

Accepted Answer

Time-Series Graph

Question 12

In a dotplot, what does each dot represent?

Accepted Answer

A single data point

Question 13

If a histogram shows a distribution where the data peaks on the left and trails off to the right, how is the distribution described?

Accepted Answer

Skewed Right

Question 14

A frequency distribution table is constructed for a café, showing customers served per hour. If the lower class limit is 15 and the class width is 5, what is the upper class limit for the first class?

Accepted Answer

Upper class limit = $$15 + 5 - 1 = 19$$

Question 15

Which of the following is NOT a characteristic of a uniform distribution in a histogram?

Accepted Answer

The data is bell-shaped.

Question 16

A time-series graph plots data points as coordinate pairs $$(x, y). $$What does $$x$$ typically represent?

Accepted Answer

$$x$$ represents time.

Question 17

If you are given a data set and asked to construct a frequency distribution with 8 classes, what is the first step?

Accepted Answer

Calculate the class width.

Question 18

Which of the following graphs is best for comparing the number of students with different hair colors in two classrooms?

Accepted Answer

Bar Graph

Question 19

In a frequency distribution, what does the relative frequency represent?

Accepted Answer

The proportion of data points in each class relative to the total.

Question 20

Which of the following is a multi-step process for constructing a frequency distribution?

Accepted Answer

1) Calculate class width; 2) Find lower class limits; 3) Find upper class limits; 4) Tally data values in each class.

Exploring Data with Tables and Graphs: Visualizing and Summarizing Data in Statistics

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