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

a) complete the frequency/relative frequency table.

class rank	frequency	relative frequency
so	5
jr	4
sr	5

b) which of the following is the correct bar chart for the given data?
two bar charts shown, one with y - axis labeled freq with values 6,5,4,3,2,1 and another with 8,6,4,2, both with class rank on x - axis (fr, so, jr, sr)

Explanation:

Part (a)

To find the relative frequency, we use the formula: Relative Frequency = $\frac{\text{Frequency}}{\text{Total Number of Observations}}$. The total number of students is 20.

Step 1: Relative Frequency for Fr

The frequency for Fr is 6. So, relative frequency = $\frac{6}{20}$ = 0.3.

Step 2: Relative Frequency for So

The frequency for So is 5. So, relative frequency = $\frac{5}{20}$ = 0.25.

Step 3: Relative Frequency for Jr

The frequency for Jr is 4. So, relative frequency = $\frac{4}{20}$ = 0.2.

Step 4: Relative Frequency for Sr

The frequency for Sr is 5. So, relative frequency = $\frac{5}{20}$ = 0.25.

Part (b)

We analyze the frequencies: Fr has frequency 6, So has 5, Jr has 4, Sr has 5. The first bar chart has Fr with height 6, So with 5, Jr with 4, Sr with 5, which matches the frequencies. The second bar chart has Fr with height 8 (incorrect) and others misaligned. So the first bar chart is correct.

Answer:

s:

Part (a)

• Fr: Relative Frequency = $\boldsymbol{0.3}$
• So: Relative Frequency = $\boldsymbol{0.25}$
• Jr: Relative Frequency = $\boldsymbol{0.2}$
• Sr: Relative Frequency = $\boldsymbol{0.25}$

Part (b)

The correct bar chart is the first one (with Fr height 6, So height 5, Jr height 4, Sr height 5).