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Rolinda’s first five Spanish test scores are 85, 85, 60, 62, and 59.
a. Find the mean, the median, and the mode of Rolinda’s Spanish test scores. Round your answers to the nearest tenth, if necessary.
b. Which of these measures best supports Rolinda’s claim that she is doing well in her Spanish class?
c. Why is Rolinda’s claim misleading?.
a.
To find the mean, we add up all the scores and divide by the total number of scores:
(85 + 85 + 60 + 62 + 59) / 5 = 70.2
The mean is 70.2.
To find the median, we first need to arrange the scores in order from lowest to highest:
59, 60, 62, 85, 85
The median is the middle score. Since there are an odd number of scores, the median is the middle score when the scores are arranged in order. In this case, the median is 62.
To find the mode, we need to identify the score that appears most frequently. In this case, there are two scores that appear twice (85 and 60) and the rest appear only once. So, there is no mode.
b.
Since Rolinda has no mode, we cannot use it to support her claim. The mean suggests she is doing well, but the median gives a more accurate representation of Rolinda’s scores since she has one really low score. The median is more resistant to outliers, so it is a better measure of central tendency in this case.
c.
Rolinda’s claim is misleading because she has one very low score, which brings down her average. The mean suggests she is doing well because the other scores are relatively high, but the median suggests otherwise since she has one score that is much lower than the others. Therefore, Rolinda’s claim cannot be fully supported by her test scores.