Given the following test scores: 5, 20, 13, 15, 12, 19, 20, 10, 17, 11, 16. What is the mean, median, and mode?

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xleb123 · Accepted Answer

To find the mean, median, and mode of the given test scores: 5, 20, 13, 15, 12, 19, 20, 10, 17, 11, 16, we can follow these steps:
Mean:
The mean is calculated by summing up all the scores and dividing by the total number of scores. Let's denote the test scores as

x_{1}, x_{2}, . . ., x_{n}

. The mean, denoted as

\bar{x}

, can be calculated as follows:

\bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n}

For the given test scores, the mean is calculated as:

\bar{x} = \frac{5 + 20 + 13 + 15 + 12 + 19 + 20 + 10 + 17 + 11 + 16}{11} = \frac{158}{11} \approx 14.36

Therefore, the mean of the test scores is approximately 14.36.
Median:
To find the median, we need to arrange the test scores in ascending order and find the middle value. If there is an odd number of scores, the median is the middle value. If there is an even number of scores, the median is the average of the two middle values.
Arranging the test scores in ascending order: 5, 10, 11, 12, 13, 15, 16, 17, 19, 20, 20
Since there are 11 scores, which is an odd number, the median is the middle value, which is the 6th score: 15.
Therefore, the median of the test scores is 15.
Mode:
The mode is the value(s) that appear(s) most frequently in the set of scores. In the given test scores, the mode is 20 since it appears twice, while all other scores appear only once.
Therefore, the mode of the test scores is 20.

Given the following test scores: 5, 20, 13,

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