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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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I apologize for the confusion. Here are the resources:
- Dot Plot: A dot plot is a type of graphical display that can be used to represent numerical data. It shows the value of each data point as a dot on a number line. In this case, the dot plot is used to display Youssef's weekly sketching data.
- Measure of Center: A measure of center is a value that summarizes the central tendency of a dataset. It represents a typical or average value in the dataset. The two main measures of center are the mean and the median.
- Mean: The mean is the sum of all the values in a dataset divided by the total number of values. It is often referred to as the average.
- Median: The median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.
Now let's answer the questions:
Question 1: Which measure of center should Youssef choose to analyze his weekly sketching goal? Why?
In this case, the dot plot shows that Youssef's data is roughly symmetric, meaning it is evenly distributed around the center. In such cases, the mean is an appropriate measure of center to use. Therefore, the correct response is A: Youssef should use the mean because the data is roughly symmetric.
Question 2: Which of the following best describes the impact of removing the values 0 and 2 from the data set?
To answer this question, we need to consider the impact of removing the values of 0 and 2.
If we remove these two values, the median will stay the same because it is determined by the middle value(s) in the dataset, and removing the lowest and second lowest values will not affect the middle. Therefore, options B and D can be eliminated.
Since the mean takes into account all the values in the dataset, removing the lowest and second lowest values (0 and 2) will increase the mean. Therefore, the correct response is B: The mean will increase and the median will stay the same.
Question 1:
To determine which measure of center Youssef should choose to analyze his weekly sketching goal, we need to consider the shape of the data. The dot plot provided shows the distribution of Youssef's data.
Looking at the dot plot, we can see that the data is roughly symmetric, with values spread out similarly on both sides of the center. In this case, Youssef should choose the mean as the measure of center because it takes into account the values of all the data points. The mean is calculated by summing all the values and dividing by the total number of values.
Therefore, the correct response is A: Youssef should use the mean because the data is roughly symmetric.
Question 2:
Removing the values 0 and 2 from the data set will impact the measure of center. Since the mean takes into account all the values, removing two values will change the sum and the total number of values.
In this case, both the mean and the median will be affected. The median is the middle value when the data is arranged in ascending order. Removing two values may shift the position of the middle value, while also changing the number of values.
Since the exact position and magnitude of the values is not known, it is difficult to determine the exact impact on the mean and median. However, removing two values will likely affect the measures of center differently.
Therefore, the correct response is C: Both the median and the mean will increase.