Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
bernice received the following scores on five science tests: 96, 77, 86, 97, and 89. which of the following statements is true?
the mode of the set of scores is 96.
the mean of the set is less than the median.
the mean and the median of the set of scores are the same.
the median of the set of scores is 86.

Explanation:

Step1: Find the mode

The mode is the number that appears most frequently. In the set {96, 77, 86, 97, 89}, each number appears only once, so there is no mode (or all numbers are modes with frequency 1). So the statement "The mode of the set of scores is 96" is false.

Step2: Find the median

First, arrange the scores in ascending order: 77, 86, 89, 96, 97. The median is the middle number. Since there are 5 numbers (odd number of observations), the median is the 3rd number, which is 89. So the statement "The median of the set of scores is 86" is false.

Step3: Find the mean

The mean is calculated as the sum of all scores divided by the number of scores. The sum of the scores is \( 96 + 77 + 86 + 97 + 89 = 445 \). There are 5 scores, so the mean is \( \frac{445}{5} = 89 \).

Step4: Compare mean and median

We found that the mean is 89 and the median is also 89. So the statement "The mean and the median of the set of scores are the same" is true, and the statement "The mean of the set is less than the median" is false.

Answer:

The mean and the median of the set of scores are the same.