Question

eva earned the following test scores in science:
82, 100, 96, 90, 91

ms. wade entered the next score as 0 because eva was absent on test day and hadnt had a chance to make up the test. which statements are true based on the data? check all that apply.

after adding the 0 test score, the mean would be the most appropriate measure of center to describe the data.

after adding the 0 test score, the mean would be affected.

after adding the 0 test score, the median would be the most appropriate measure of center to describe the data.

before the missed test, evas median score was 96.

before the missed test, evas median score was 91.

before the missed test, evas mean score was 91.8.

Explanation:

Step1: Calculate the original mean

The original scores are \(82\), \(100\), \(96\), \(90\), \(91\).
The mean formula is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\).
Here \(n = 5\), \(\sum_{i=1}^{5}x_{i}=82 + 100+96 + 90+91=459\).
The original mean \(\bar{x}_{1}=\frac{459}{5}=91.8\).

Step2: Calculate the original median

Arrange the original data in ascending order: \(82\), \(90\), \(91\), \(96\), \(100\).
The median formula for \(n = 5\) (odd) is \(M=\frac{n + 1}{2}\) - th term.
So the original median \(M_{1}=91\).

Step3: Analyze the effect of adding \(0\)

After adding \(0\), the new data set is \(0\), \(82\), \(90\), \(91\), \(96\), \(100\).
The new mean \(\bar{x}_{2}=\frac{459+0}{6}=76.5\).
The new median (for \(n = 6\) (even)) is \(M_{2}=\frac{90 + 91}{2}=90.5\).
Since \(0\) is an extreme value (outlier), the median is a better measure of central tendency than the mean when there is an outlier.

Answer:

• After adding the \(0\) test score, the mean would be affected.
• After adding the \(0\) test score, the median would be the most appropriate measure of center to describe the data.
• Before the missed test, Eva's median score was \(91\).
• Before the missed test, Eva's mean score was \(91.8\).