Questions: The table below shows the scores of a group of students on a 10-point quiz. Test Score Frequency 3 1 4 3 5 2 6 4 7 0 8 2 9 2 10 3 The mean score on this test is: The median score on this test is: Round your answer to one decimal place if rounding is necessary.

Solution Steps

To find the mean score \( \mu \), we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( \sum_{i=1}^N x_i \) is the sum of all test scores and \( N \) is the total number of scores.

Calculating the sum of the scores:

\[ \sum_{i=1}^{17} x_i = 3 \times 1 + 4 \times 3 + 5 \times 2 + 6 \times 4 + 7 \times 0 + 8 \times 2 + 9 \times 2 + 10 \times 3 = 113 \]

The total number of scores \( N \) is:

\[ N = 1 + 3 + 2 + 4 + 0 + 2 + 2 + 3 = 17 \]

Thus, the mean score is:

\[ \mu = \frac{113}{17} = 6.6 \]

To find the median score, we first sort the data:

\[ \text{Sorted data} = [3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 8, 8, 9, 9, 10, 10, 10] \]

The median is the value at the position given by the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (17 + 1) = 9.0 \]

Since the rank is 9, we take the value at the 9th position in the sorted list, which is:

\[ \text{Median} = 6 \]

Final Answer