Normal Investigation
Here, we will discover how the normal distribution is distributed, especially with proportions.
For normal distributions, the proportion of data is approximately equal for all normal distributions, considering units of standard deviation from the mean.
We can find these proportions through advanced calculus, but it is beyond our current level, so instead, we will use data to help approximate these.
In the app below, there are 1000 data points, which are approximately normal, and plotted with a bar chart. We will be finding how much of the data lays between 1, 2, and 3 standard deviations away from the mean.
Follow the questions below, answering them in the worksheet provided.
Question 1: Look at the bar chart below. Is it approximately symmetrical? What is the mean? How close is it to the perfect normal curve (shown in grey)?
Question 2: Push the button "Add Statistics". Copy down the mean and standard deviation.
Question 3: We will be investigating one, two, and three standard deviations away from the mean. Calculate these values, and add them to the table in the worksheet.
Question 4: You can now move the red dots, which create a red area, and the app will count the number of data points contained in the red area. Set the red areas to the three ranges in your worksheet, and record the % of data points for each range.
Question 5: Push "Next Data Set", and then push "New Data Set". Repeat questions 2-4.
Question 6: Repeat question 5 one more time.
Question 7: What patterns do you notice?