Question

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question 11: abigail scored the following grades on her first 8 math exams for the school year. her scores are shown below.
70, 72, 78, 80, 80, 82, 84, 90
abigail took one last test and received a 94. does the added test score change the mean, median, or both? explain your answer.

Explanation:

Step1: Calculate the original mean

First, find the sum of the original 8 scores: \(70 + 72 + 78 + 80 + 80 + 82 + 84 + 90\)
\(= 70+72 = 142\); \(142+78 = 220\); \(220+80 = 300\); \(300+80 = 380\); \(380+82 = 462\); \(462+84 = 546\); \(546+90 = 636\)
The original mean is \(\frac{636}{8}=79.5\)

Step2: Calculate the new mean

Add the new score (94) to the sum: \(636 + 94 = 730\)
Now there are 9 scores, so the new mean is \(\frac{730}{9}\approx81.11\) (the mean changes)

Step3: Find the original median

For 8 scores (even number), the median is the average of the 4th and 5th terms. The ordered scores: 70, 72, 78, 80, 80, 82, 84, 90.
4th term = 80, 5th term = 80. Median = \(\frac{80 + 80}{2}=80\)

Step4: Find the new median

With 9 scores (odd number), the median is the 5th term. The new ordered scores: 70, 72, 78, 80, 80, 82, 84, 90, 94.
5th term is 80 (the median remains 80)

Answer:

The added test score changes the mean (the original mean was 79.5 and the new mean is approximately 81.11) but does not change the median (the original median was 80 and the new median is still 80). So it changes the mean, and the median stays the same.