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 mean of the set is less than the median. the median of the set of scores is 86. the mean and the median of the set of scores are the same. the mode of the set of scores is 96.

Explanation:

Step1: Order the scores

First, we order the scores from least to greatest: \( 77, 86, 89, 96, 97 \).

Step2: Find the median

The median is the middle value of a sorted set. For a set with 5 values (odd number), the median is the 3rd value. So the median is \( 89 \).

Step3: Calculate the mean

The mean is calculated by summing all the values and dividing by the number of values. 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: Analyze the mode

The mode is the value that appears most frequently. In this set, each score appears only once, so there is no mode (or all scores are modes with frequency 1). But since 96 appears only once, the statement "The mode of the set of scores is 96" is false.

Step5: Compare mean and median

We found that the mean is \( 89 \) and the median is \( 89 \), so the mean and the median are the same. The other statements: "The mean of the set is less than the median" is false (they are equal), "The median of the set of scores is 86" is false (median is 89), and "The mode of the set of scores is 96" is false. So the true statement is "The mean and the median of the set of scores are the same."

Answer:

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