Question

aiden’s test scores for the same term were 30, 70, 90, 90, 91, and 99. which measure of central tendency would aiden want his teacher to base his grade on? justify your think explain your reasoning: _____________ ___________ ___________ mean: 74.2 median: 90 mode: 90 look at aiden’s test scores again. i want you to pretend you are the teacher and you need to assign a final semester grade for aiden, based on his test scores. you can use one of the 3 measures of central tendency or you can arrive at a grade based on your own “system”. once you have decided on a grade, explain what method you used to determine his grade. i would give aiden a % or i would give him a (a,b,c,d,f) explain why: ___________ _____________

Explanation:

Step1: Calculate the mean

The mean is the sum of all values divided by the number of values. The scores are 30, 70, 90, 90, 91, 99. The sum is \(30 + 70 + 90 + 90 + 91 + 99 = 470\). There are 6 scores, so the mean is \(\frac{470}{6} \approx 78.33\) (wait, the original had 74.2, maybe a miscalculation earlier; let's recalculate: 30+70=100, 100+90=190, 190+90=280, 280+91=371, 371+99=470. 470/6 ≈78.33).

Step2: Calculate the median

To find the median, we first order the data (already ordered: 30, 70, 90, 90, 91, 99). Since there are 6 values (even number), the median is the average of the 3rd and 4th values. So \(\frac{90 + 90}{2} = 90\).

Step3: Determine the mode

The mode is the most frequently occurring value. 90 appears twice, others once, so mode is 90.

For Aiden's preference: The mean is lower due to the low score (30), while median and mode are higher (90). So Aiden would want median or mode, as they are not affected by the outlier (30) and give a higher grade.

For the teacher's grade: Using median (90) or mode (90) might be fairer if we consider that the 30 is an outlier, or mean if we include all scores. Let's say using median: grade 90, because the median represents the middle value, and the low score (30) is an outlier that skews the mean. Or mean: ~78, but that's lower. Alternatively, dropping the lowest score (30) and averaging the rest: (70+90+90+91+99)/5 = (440)/5 = 88. But the question allows using a measure or own system.

Answer:

First Part (Aiden's Preference)

Aiden would want his teacher to base his grade on the median (or mode) because the mean is lowered by the outlier (30), while median (90) and mode (90) are higher and represent the central tendency of his better scores.

Second Part (Teacher's Grade)

I would give Aiden a \(\boldsymbol{90}\%\) (using median) because the median (\(90\)) is the middle value when ordered, and the score of \(30\) is an outlier that disproportionately lowers the mean. The median better represents the typical performance of Aiden’s other scores (most scores are 90 or above, except 30 and 70, but the middle is 90).

(Or using mode: 90, same reasoning. If using mean: ~78, but that’s lower due to the outlier.)