Q: When constructing a frequency polygon, which value is plotted on the x-axis for each class?

The midpoint of the class interval, calculated as $$\frac{\text{lower limit} + \text{upper limit}}{2}.$$

Question 1

Which of the following best describes a frequency polygon?

Accepted Answer

A graph that uses points connected by straight lines to represent frequencies for each class midpoint.

Question 2

When constructing a frequency polygon, which value is plotted on the x-axis for each class?

Accepted Answer

The midpoint of the class interval, calculated as $$\frac{	ext{lower limit} + 	ext{upper limit}}{2}.$$

Question 3

Given the following age distribution in a public bus: 0-12 (6), 13-24 (8), 25-37 (7), 38-50 (5), what is the midpoint for the 13-24 age group?

Accepted Answer

$$\frac{13 + 24}{2} = 18.5$$

Question 4

A frequency polygon is most useful for which of the following purposes?

Accepted Answer

Comparing the distribution of two or more datasets on the same graph.

Question 5

In the frequency polygon for test scores, the highest frequency occurs in the interval 47 to 57. What does this indicate about the test scores?

Accepted Answer

Most students scored between 47 and 57.

Question 6

If you are given the following frequency table for ages on a subway: 22-25 (2), 26-29 (4), 30-33 (7), 34-37 (10), 38-41 (8), 42-45 (5), 46-49 (3), 50-53 (1), which age group has the highest frequency?

Accepted Answer

34-37

Question 7

When plotting a frequency polygon, why is it important to start and end the graph at the midpoints of intervals with zero frequency?

Accepted Answer

To ensure the polygon is closed and accurately represents the distribution.

Question 8

Suppose you have two frequency polygons representing the age distribution of people on two different buses. What feature would you compare to determine which bus has a younger population?

Accepted Answer

The position of the peak (mode) on the x-axis.

Question 9

Given the frequency polygon for test scores, if the frequencies for intervals 37-47 and 47-57 are 5 and 9 respectively, what is the total number of students who scored between 37 and 57?

Accepted Answer

$$5 + 9 = 14$$

Question 10

If the frequency polygon for ages in a subway car shows a sharp peak at the midpoint 35.5, what does this suggest about the age distribution?

Accepted Answer

Most people in the subway car are around 35 years old.

Question 11

Which of the following is a key difference between a histogram and a frequency polygon?

Accepted Answer

A histogram uses bars, while a frequency polygon uses points connected by lines.

Question 12

If the frequency polygon for test scores is skewed to the right, what does this indicate about the distribution of scores?

Accepted Answer

Most students scored lower, with a few high scores.

Question 13

A teacher wants to compare the test score distributions of two classes. Which graphical method would be most appropriate?

Accepted Answer

Plotting both frequency polygons on the same axes.

Question 14

If the frequency polygon for ages in a public bus has two peaks, what does this suggest about the age distribution?

Accepted Answer

There are two age groups with high frequencies (bimodal distribution).

Question 15

Given the following class intervals and frequencies: 10-19 (3), 20-29 (7), 30-39 (12), 40-49 (8), what is the midpoint for the interval 30-39?

Accepted Answer

$$\frac{30 + 39}{2} = 34.5$$

Question 16

A frequency polygon is constructed from a frequency table. What is the first step in plotting the points?

Accepted Answer

Calculate the midpoint for each class interval.

Question 17

If the frequency polygon for test scores shows a flat line across all intervals, what does this indicate?

Accepted Answer

The frequencies are equal for all score intervals (uniform distribution).

Question 18

Which of the following is NOT a step in constructing a frequency polygon?

Accepted Answer

Drawing bars for each class interval.

Question 19

A frequency polygon for ages in a subway car shows the following frequencies: 22-25 (2), 26-29 (4), 30-33 (7), 34-37 (10), 38-41 (8). What is the total number of people aged between 26 and 41?

Accepted Answer

$$4 + 7 + 10 + 8 = 29$$

Question 20

If a frequency polygon is constructed from grouped data, what is the effect of using wider class intervals?

Accepted Answer

The polygon will be less detailed and may hide important features of the distribution.

Frequency Polygons: Construction and Interpretation

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