Mean & Standard Deviation Exploration Name: Directions For this assignment you will compare the dot plots provided to answer questions. The blue dots represent sample data values. When two data values are the same, they stack one on top of the other to show frequency as a height. The sample mean ( x ) and sample standard deviation ( s ) are given for all dot plots on this worksheet. Questions 1. Compare the following two dot plots. and x 2.5 s 2.09 x 2.7 and s 2.23 a. What happens to the sample mean when a point was moved to the right? b. What happens to the sample standard deviation when a point was moved to the right? 2. Compare the following two dot plots. and x 2.5 s 2.09 x 2.25 and s 1.94 a. What happens to the sample mean when a point was moved to the left? b. What happens to the sample standard deviation when a point was moved to the left? Mean & Standard Deviation Exploration Name: 3. Use the following dot plot. x 1 and s 1.95 a. How would you describe the shape of the above distribution (left/right skewed, uniform, bell-shaped, or bimodal)? 4. The following dot plot has been rearranged from #3 to have a different distribution, but the same sample mean. x 1 and s 1.41 a. What is the shape of your new distribution(left/right skewed, uniform, bell-shaped, or bimodal)? 5. Create a rough sketch of a highly left-skewed distribution below. a. In a highly left-skewed distribution, are the majority of the data points to the left or right of the mean? Mean & Standard Deviation Exploration Name: 6. The following dot plot has a sample mean of 1 and the distribution is bell-shaped. x 1 and s 1.3 a. What is the sample standard deviation of this plot? b. Compare the above dot plot to this new dot plot. The mean is still the same, but the standard deviation is smaller. What changes had to be made to the dot plot for this to occur? x 1 and s 0.79 c. Compare the original dot plot for number 6 to this dot plot. The mean is still the same, but the standard deviation is larger. What changes had to be made to the dot plot for this to occur? x 1 and s 2.18 Mean & Standard Deviation Exploration Name: 7. Without dot plots, imagine the two distributions below: a. x =1.5, s=1 b. x =1.5, s=3 What is the difference between how these two distributions would look