1. A. Create a set of 5 points that are very close together and record the stand
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Question
1. A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far away from the original 5 and record the new standard deviation. What is the impact of the new point on the standard deviation? Do not just give a numerical value for the change. Explain in sentence form what happened to the standard deviation. (4 points) B. Create a data set with 8 points in it that has a mean of approximately 10 and a standard deviation of approximately 1. Use the second chart to create a second data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4. What did you do differently to create the data set with the larger standard deviation? (4 points) 2. Go back to the spreadsheet and clear the data values from Question 1 from the data column and then put values matching the following data set into the data column for the first graph. (8 points) 50, 50, 50, 50, 50. Notice that the standard deviation is 0. Explain why the standard deviation for this one is zero. Do not show the calculation. Explain in words why the standard deviation is zero when all of the points are the same. If you don’t know why, try doing the calculation by hand to see what is happening. If that does not make it clear, try doing a little research on standard deviation and see what it is measuring and then look again at the data set for this question. 3. Go back to the spreadsheet one last time and put each of the following three data sets into one of the graphs. Record what the standard deviation is for each data set and answer the questions below. Data set 1: 0, 0, 0, 100, 100, 100 Data set 2: 0, 20, 40, 60, 80, 100 Data set 3: 0, 40, 45, 55, 60, 100 Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists. Do not give your calculations in your answer—explain in sentence form. (8 points) For the last 2 questions, use the Project 1 Data Set. 4. Explain what an outlier is. Then, if there are any outliers in the Project 1 Data Set, what are they? If there are no outliers, say no outliers. (4 points) 5. Which 4 states have temperatures that look to be the most questionable or the most unrealistic to you? Explain why you selected these 4 states. For each state, give both the name and the temperature. (4 points)
Explanation / Answer
1.A. Let the data set be 8,9,10,11 and 12.
Standard deviation = 1.414
Let the 6th point be 50
The standard deviation of the new data set 8,9,10,11,12 and 50 is 14.963
The standard deviation, the square root of the variance, is a measure of how widely spreadout the data are, around the mean.
In the first data set, the mean is 10 and the data are compactly sperad out in a narrow range around the mean, so the variance and the standard deviations are small.
In the second data set, due to the presence of a larger number 50, the mean is 16.67 and the data are relatively widely spread out around the mean,hence we have a larger variance and standard deviation as compared to the previous data set.
B. An example of a data set with mean approx 10 and standard deviation approx. 1 is:
8.5, 8.8, 9.4, 9.8, 10.2, 10.6, 11.2, 11.5
Mean is 10 and standard deviation is 1.01
Another example of data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4 is:
4,6,7,9,11,12,15,16
This data set has mean =10 and standard deviation = 4
We had to spread out the 1st set of data to get the second set of data with a larger standard deviation.
2. For the data set 50, 50, 50, 50, 50, the standard deviation is 0. This is because all the data have the same value, so there is no deviation of each data from the mean, which is 50 in this case.
Since the deviation of each data point in the above set is 0 from the mean, we have 0 variance and 0 standard deviation.
3. Data set 1: 0, 0, 0, 100, 100, 100; Standard deviation = 50
Data set 2: 0, 20, 40, 60, 80, 100; standard deviation= 34.16
Data set 3: 0, 40, 45, 55, 60, 100; standard deviation = 29.58
I am not sure what chart the question refers to, but in the first data set, there are only 2 data values and each data point has a spread of 50 from the mean,50. So the standard deviation is high, 50.
In the second data set, the spread of each data points from the mean, 50 are 50,30,10,10,30 and 50. So the data are relatively more compact as compared to the first data set.
In the third data set, the spread of each data point from the mean 50 are 50,10,5,5,10 and 50. So the spreads are still lesser in this case. So for this data set 3, we have the least standard deviation among the 3 data sets.
The wider the data points are spread out from the mean, the larger would be the standard deviation.
The Project 1 data set are missing, so can't answer the last 2 questions.
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