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Question 1
Youssef has a goal of drawing in his sketchbook at least 10 times per week to improve his skills. He records how many times he was able to sketch each week for 18 weeks. The dot plot below displays his data.
PART A
Which measure of center should Youssef choose to analyze his weekly sketching goal? Why?
Responses
A Youssef should use the mean because the data is roughly symmetric.Youssef should use the mean because the data is roughly symmetric.
B Youssef should use the median because the data is roughly symmetric.Youssef should use the median because the data is roughly symmetric.
C Youssef should use the mean because the data is skewed left.Youssef should use the mean because the data is skewed left.
D Youssef should use the median because the data is skewed left.Youssef should use the median because the data is skewed left.
Question 2
PART B
Which of the following best describes the impact of removing the values 0 and 2 from the data set?
Responses
A The median will increase and the mean will stay the same.The median will increase and the mean will stay the same.
B The mean will increase and the median will stay the same.The mean will increase and the median will stay the same.
C Both the median and the mean will increase.Both the median and the mean will increase.
D The mean will decrease and the median will stay the same.The mean will decrease and the median will stay the same.
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Question 1:
The correct answer is B. Youssef should use the median because the data is roughly symmetric. The dot plot shows that there are an equal number of values above and below the center, indicating symmetry. In this case, the median would provide a better measure of center than the mean.
Question 2:
The correct answer is A. The median will increase and the mean will stay the same. Removing the values 0 and 2 from the data set will affect the median but not the mean. The median is the middle value in a data set, so removing the values 0 and 2 will increase the middle value and therefore increase the median. However, the mean is not affected by the position of the values, so it will stay the same.