the scores for 21 students on an exam are summarized in the stemplot below. exam scores 4|9 5 6|9 7|1 2 5 5…
the scores for 21 students on an exam are summarized in the stemplot below. exam scores 4|9 5 6|9 7|1 2 5 5 6 7 8|0 1 2 4 5 5 6 9 9 9|0 1 4 7 key: 9|0 = 90% on the exam the teacher realizes that a mistake was made and the student whose score was recorded as 49% should have been 69%. if the mistake is corrected, what effect will this have on the mean and median scores? the mean and median will both increase. neither the mean nor the median will change. the mean will increase but the median will decrease. the mean will increase but the median will be unchanged.
Answer
Explanation:
Step1: Recall mean and median concepts
Mean is sum of all values divided by number of values. Median is middle - value when data is ordered.
Step2: Analyze effect on mean
The sum of scores will increase since 49 is replaced by 69. With number of students (21) constant, using $\text{Mean}=\frac{\text{Sum of scores}}{\text{Number of students}}$, the mean will increase.
Step3: Analyze effect on median
There are $n = 21$ data - points. The median is the $\left(\frac{n + 1}{2}\right)=\frac{21+1}{2}=11$th value when data is ordered. Since 49 was the lowest value and 69 is still less than most of the other values, the order of the 11th value in the ordered list of scores does not change. So the median remains the same.
Answer:
The mean will increase but the median will be unchanged.