Q: If you were to calculate the relative frequency for the 40–44 age group, which formula would you use?

$$\text{Relative frequency} = \frac{14,558}{\text{Total number of mothers}}$$

Question 1

Given the data on the number of mothers in the United States, ages 15–54, who had their fourth child in 2016, which of the following is the correct lower class limit for the second class if the classes are defined as 15–19, 20–24, 25–29, etc.?

Accepted Answer

20

Question 2

What is the class width for the age intervals in the provided data table?

Accepted Answer

$$5$$

Question 3

If you were to construct a frequency histogram from the data, what would the height of the bar for the 30–34 age group represent?

Accepted Answer

The number of mothers aged 30–34 who had their fourth child in 2016

Question 4

How would you calculate the relative frequency for the 25–29 age group using the data provided?

Accepted Answer

Divide the number of mothers in the 25–29 group by the total number of mothers in all age groups

Question 5

Which of the following best describes the shape of the distribution for the number of mothers by age group who had their fourth child in 2016?

Accepted Answer

Skewed right

Question 6

Suppose you want to create a new frequency table with class widths of 10 years (e.g., 15–24, 25–34, etc.). What would be the frequency for the 25–34 class?

Accepted Answer

$$84,217 + 101,070 = 185,287$$

Question 7

If you were to plot a relative frequency histogram for this data, what would the sum of the heights of all the bars be?

Accepted Answer

$$1$$

Question 8

Which of the following statements about class limits is correct for the given data?

Accepted Answer

The lower class limit of the first class is 15 and the upper class limit is 19

Question 9

Why might different frequency distributions be constructed for the same data set?

Accepted Answer

Because the choice of class width and lower class limit can be arbitrary and may highlight different patterns in the data

Question 10

If you wanted to use JMP to create a histogram of this data, which of the following would you need to do first?

Accepted Answer

Enter the age groups and corresponding frequencies into the software

Question 11

A student claims that the distribution of mothers by age group is uniform. Which of the following best refutes this claim?

Accepted Answer

The frequencies vary greatly between age groups, with a peak in the 30–34 group

Question 12

If you were to calculate the relative frequency for the 40–44 age group, which formula would you use?

Accepted Answer

$$	ext{Relative frequency} = \frac{14,558}{	ext{Total number of mothers}}$$

Question 13

Which of the following is NOT a possible shape for a distribution as described in the study materials?

Accepted Answer

Triangular

Question 14

If the data were instead evenly spread across all age groups, what would the shape of the distribution be called?

Accepted Answer

Uniform

Question 15

Suppose you want to compare the proportion of mothers aged 25–29 to those aged 35–39. Which calculation would you use?

Accepted Answer

$$\frac{84,217}{63,461}$$

Question 16

If you were to add a new class for ages 55–59 with a frequency of 10, how would this affect the shape of the distribution?

Accepted Answer

It would have little effect, as the frequency is very low compared to other classes

Organizing Quantitative Data: Frequency Tables and Histograms

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