the table below shows the scores of a group of students on a 10 - point quiz.\n| test score | frequency |\n|…

Explanation:

Step1: Calculate the sum of the products of scores and frequencies

First, find the product of each test - score and its frequency: For score 3: $3\times3 = 9$ For score 4: $4\times7=28$ For score 5: $5\times1 = 5$ For score 6: $6\times1 = 6$ For score 7: $7\times3 = 21$ For score 8: $8\times4 = 32$ For score 9: $9\times2 = 18$ For score 10: $10\times4 = 40$ The sum of these products is $9 + 28+5 + 6+21+32+18+40=159$.

Step2: Calculate the total frequency

The total frequency is $3 + 7+1 + 1+3+4+2+4=25$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}$, where $x_i$ is the score and $f_i$ is the frequency. So the mean is $\frac{159}{25}=6.36$.

Step4: Calculate the median

Arrange the data in ascending - order. The total number of data points $n = 25$ (an odd number). The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{25+1}{2}=13$-th value. Count the frequencies: The first 3 values have a score of 3 (total of 3 values so far). The next 7 values have a score of 4 (total of $3 + 7=10$ values so far). The next 1 value has a score of 5 (total of $10 + 1=11$ values so far). The next 1 value has a score of 6 (total of $11+1 = 12$ values so far). The next 3 values have a score of 7, and the 13 - th value falls within this group. So the median is 7.

Answer:

The mean score on this test is: $6.36$ The median score on this test is: $7$