Questions: Question Jennifer is a teacher who is reviewing the average scores on the 10 tests in her class last year. The average scores are shown below. Average Test Scores 82 81 79 79 78 80 77 78 80 76 Use a calculator to create a relative frequency distribution for the data. What is the relative frequency of an average test score of at least 80? Provide your answer below:

Solution Steps

To analyze the average test scores, we first calculate the frequency of each score. The average test scores are:

$$\{82, 81, 79, 79, 78, 80, 77, 78, 80, 76\}$$

The frequency distribution is as follows:

• $82$ appears $1$ time
• $81$ appears $1$ time
• $79$ appears $2$ times
• $78$ appears $2$ times
• $80$ appears $2$ times
• $77$ appears $1$ time
• $76$ appears $1$ time

Next, we calculate the relative frequency for each score by dividing the frequency of each score by the total number of scores, which is $10$:

$$\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Scores}}$$

The relative frequency distribution is:

\begin{align_} 82 & : \frac{1}{10} = 0.1 \\ 81 & : \frac{1}{10} = 0.1 \\ 79 & : \frac{2}{10} = 0.2 \\ 78 & : \frac{2}{10} = 0.2 \\ 80 & : \frac{2}{10} = 0.2 \\ 77 & : \frac{1}{10} = 0.1 \\ 76 & : \frac{1}{10} = 0.1 \\ \end{align_}

To find the relative frequency of scores that are at least $80$, we sum the relative frequencies of the scores $80$ and $82$:

$$\text{Relative Frequency of scores} \geq 80 = P(80) + P(82)$$

Substituting the values:

$$= 0.2 + 0.1 = 0.3$$

Thus, the relative frequency of average test scores of at least $80$ is $0.3$.

Final Answer