anya plays one round of her favorite online game every day. one week, she played 7 rounds and scored between…
anya plays one round of her favorite online game every day. one week, she played 7 rounds and scored between 120 and 300 points each round. she calculated the mean and median of those scores. then, anya found out that the day she scored 300 points was a special \double points\ day, so she actually earned 600 points, not 300. how will this amount increasing affect the mean and median? choose 1 answer: a both the mean and median will increase. b the mean will stay the same, and the median will increase. c the mean will increase, and the median will decrease. d the mean will increase, and the median will stay the same.
Answer
Explanation:
Step1: Recall the formula for the mean
The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 7$. Let the sum of the original 7 - scores be $S$. The original mean $\bar{x}_1=\frac{S}{7}$. When the score of 300 is changed to 600, the new sum of scores is $S-300 + 600=S + 300$. The new mean $\bar{x}_2=\frac{S + 300}{7}=\frac{S}{7}+\frac{300}{7}$. So the mean increases.
Step2: Recall the concept of the median
The median is the middle - value when the data is arranged in ascending or descending order. Since we have 7 (an odd number) data points, the median is the 4th - ranked value when the scores are ordered. Changing the largest value (from 300 to 600) does not change the position of the middle - value. So the median stays the same.
Answer:
D. The mean will increase, and the median will stay the same.