Answer :
Final Answer:
The option b. "The mode is 82" is true about Danielle's test scores after scoring an 82 on her last test.
Explanation:
The mode of a set of numbers is the value that appears most frequently in the data. In this case, Danielle's test scores are 77, 82, 91, 99, and 82. The number 82 appears twice, which is more frequent than any other score, making it the mode.
Let's briefly consider the other options:
a. The mean (average) of the scores is calculated by adding all the scores and dividing by the number of scores. Adding an 82 to the set of scores does not necessarily change the mean, as it depends on the specific values of the other scores.
c. The mean can remain unchanged if the other scores are balanced in a way that compensates for the addition of an 82.
d. The median is the middle value when the scores are arranged in order. If the scores are arranged as 77, 82, 82, 91, and 99, the median remains 82, so it doesn't necessarily increase either.
Therefore, the only statement that is definitively true based on the information provided is that the mode of Danielle's test scores is 82. This means that 82 is the score that appears most frequently in her test results. (Option b)
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