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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.
D The mean will decrease and the median will stay the same.
do part a too
B Youssef should use the median because the data is roughly symmetric.
To answer these questions, first let's understand some concepts:
1. Mean: The mean is a measure of center that is calculated by summing all the values and dividing by the total number of values. It is affected by the values themselves and can be influenced by outliers.
2. Median: The median is another measure of center that represents the middle value of a data set when it is arranged in numerical order. It is not affected by extreme values, making it a good choice when the data has outliers.
Now let's analyze the given information to answer the questions:
Question 1:
Youssef wants to analyze his weekly sketching goal, and we are given the dot plot of his data. To choose the appropriate measure of center, we need to consider the symmetry of the data.
Looking at the dot plot, if the data is roughly symmetric, it means that it is evenly distributed around a central value. In this case, both the mean and the median would be good choices.
Since the data appears to be roughly symmetric, the correct answer is A. Youssef should use the mean because the data is roughly symmetric.
Question 2:
We are asked about the impact of removing the values 0 and 2 from the data set on the median and mean.
If we remove these values, the data set will change, potentially affecting the measures of center.
To analyze this, let's consider the effect on the mean and median:
- Mean: The mean will be affected by the values themselves. If we remove 0 and 2, which are low values, the mean will likely increase as the remaining values are higher.
- Median: The median represents the middle value, so if we remove 0 and 2, the middle value may not change, especially if other values are already higher or lower.
Based on this analysis, the correct answer is B. The mean will increase and the median will stay the same.
Remember, when analyzing the impact of removing or adding values, it is important to consider the characteristics of the data set and the measures of center being used.