Question

the class ranks of a very small high school with 20 students are shown in the table below.

fr fr fr so so
so sr so sr jr
jr fr so so so
fr sr fr fr so

a) complete the frequency/relative frequency table.

class rank	frequency	relative frequency
so	8
jr	2
sr	3

b) which of the following is the correct bar chart for the given data?

Explanation:

Part (a) - Completing the Relative Frequency Table

Relative frequency is calculated as the frequency of a class rank divided by the total number of students. The total number of students is 20 (given in the problem: "a very small high school with 20 students").

Step 1: Relative Frequency for "Fr"

The frequency of "Fr" is 7. To find the relative frequency, we divide the frequency by the total number of students (20).
\[
\text{Relative Frequency for Fr} = \frac{7}{20} = 0.35
\]

Step 2: Relative Frequency for "So"

The frequency of "So" is 8. Divide by 20:
\[
\text{Relative Frequency for So} = \frac{8}{20} = 0.4
\]

Step 3: Relative Frequency for "Jr"

The frequency of "Jr" is 2. Divide by 20:
\[
\text{Relative Frequency for Jr} = \frac{2}{20} = 0.1
\]

Step 4: Relative Frequency for "Sr"

The frequency of "Sr" is 3. Divide by 20:
\[
\text{Relative Frequency for Sr} = \frac{3}{20} = 0.15
\]

Part (b) - Correct Bar Chart

To determine the correct bar chart, we analyze the frequencies:

• "Fr" has a frequency of 7
• "So" has a frequency of 8 (the highest)
• "Jr" has a frequency of 2 (the lowest)
• "Sr" has a frequency of 3

The bar chart should have bars with heights corresponding to these frequencies. So, the bar for "So" should be the tallest, followed by "Fr", then "Sr", and the shortest bar for "Jr".

Final Answers

Part (a)

Class Rank	Frequency	Relative Frequency
So	8	0.4
Jr	2	0.1
Sr	3	0.15

Part (b)

The correct bar chart will have:

• A bar for "Fr" with height 7
• A bar for "So" with height 8 (tallest)
• A bar for "Jr" with height 2 (shortest)
• A bar for "Sr" with height 3

(Note: Since the actual bar chart options are not provided here, the key is to match the bar heights to the frequencies calculated above.)

Answer:

To determine the correct bar chart, we analyze the frequencies:

• "Fr" has a frequency of 7
• "So" has a frequency of 8 (the highest)
• "Jr" has a frequency of 2 (the lowest)
• "Sr" has a frequency of 3

The bar chart should have bars with heights corresponding to these frequencies. So, the bar for "So" should be the tallest, followed by "Fr", then "Sr", and the shortest bar for "Jr".

Final Answers

Part (a)

Class Rank	Frequency	Relative Frequency
So	8	0.4
Jr	2	0.1
Sr	3	0.15

Part (b)

The correct bar chart will have:

• A bar for "Fr" with height 7
• A bar for "So" with height 8 (tallest)
• A bar for "Jr" with height 2 (shortest)
• A bar for "Sr" with height 3

(Note: Since the actual bar chart options are not provided here, the key is to match the bar heights to the frequencies calculated above.)