Q: If the frequency for the class 9-13 is 12, and the total number of students is 47, what is the percentage frequency for this class?

$$\frac{12}{47} \times 100 \approx 25.53\%$$

Question 1

Given the following data set representing the number of pushups completed by 7th graders: 5, 8, 6, 10, 12, 22, 29, 6, 7, 8, 9, 19, 11, 11, 6, 11, 12, 11, 16, 18, 12, 15, 14, 16, 20, 21, 20, 16, 15, 14, 8, 8, 11, 20, 17, 13, 15, 14, 18, 20, 11, 19, 21, 22, 7, 9, 4. What is the range of this data set?

Accepted Answer

$$29 - 4 = 25$$

Question 2

If you are to construct a histogram with 5 classes for the pushup data, what is the appropriate class width? (Use the formula: $$	ext{Class Width} = \frac{	ext{Range}}{	ext{Number of Classes}}$$, and round up to the next whole number.)

Accepted Answer

$$\frac{25}{5} = 5 (so $$class width is 5)

Question 3

Which of the following is the correct formula for determining the lower class limit of the first class in a histogram?

Accepted Answer

The minimum value in the data set

Question 4

Suppose you have constructed the following 5 classes for the pushup data: 4-8, 9-13, 14-18, 19-23, 24-28. If a student completed 22 pushups, to which class does this value belong?

Accepted Answer

19-23

Question 5

What is the main purpose of constructing a histogram for the pushup data?

Accepted Answer

To visually display the frequency distribution of the data

Question 6

If the histogram of the pushup data is skewed to the right, what does this indicate about the distribution of pushup counts among students?

Accepted Answer

Most students did fewer pushups, with a few students doing much more

Question 7

Which of the following best describes a class boundary in a histogram?

Accepted Answer

A value that separates one class from another, typically halfway between upper and lower class limits

Question 8

If you were to calculate the relative frequency for the class 14-18, and there are 10 students in this class out of 47 total students, what is the relative frequency?

Accepted Answer

$$\frac{10}{47} \approx 0.213$$

Question 9

Which of the following is NOT a step in constructing a histogram?

Accepted Answer

Calculating the mean of the data

Question 10

If the class intervals for the histogram are 4-8, 9-13, 14-18, 19-23, and 24-28, what is the midpoint of the class 14-18?

Accepted Answer

$$\frac{14 + 18}{2} = 16$$

Question 11

A student claims that the histogram for the pushup data should have overlapping classes to ensure all data is included. Is this correct?

Accepted Answer

No, classes in a histogram should not overlap to avoid double-counting data points

Question 12

If you want to compare the distribution of pushups between two different classes using histograms, what should you ensure about the histograms?

Accepted Answer

Both histograms should use the same class width and class limits

Question 13

If the frequency for the class 9-13 is 12, and the total number of students is 47, what is the percentage frequency for this class?

Accepted Answer

$$\frac{12}{47} 	imes 100 \approx 25.53\%$$

Question 14

Which of the following statements about histograms is TRUE?

Accepted Answer

The area of each bar is proportional to the frequency of the class it represents

Question 15

If a student wants to estimate the mode of the pushup data using the histogram, what should they look for?

Accepted Answer

The class with the highest frequency

Histograms and Data Grouping: Constructing a 5-Class Histogram

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