- Understand the meaning of normal distribution and bell-shape.
- Estimate the mean and the standard deviation of a normal distribution.
Now that you have created your plot on a large sheet of grid paper, can you describe the shape of the plot? Do the dots seem to be clustered around 1 spot (value) on the chart? Do some dots seem to be far away from the clustered dots? After you have made all the necessary observations to answer these questions, pick 2 numbers from the chart to complete this statement:
“The typical measurement of the diameter is approximately______inches, give or take______inches.”
We will complete this statement later in the lesson.
The shape below should be similar to the shape that has been created with the dot plot.
When you made the observations regarding the measurements of the diameter of the basketball, you must have noticed that they were not all the same. In spite of the different measurements, you should have seen that the majority of the measurements clustered around the value of 9.4 inches. This value represents the approximate diameter of a basketball. Also, you should have noticed that a few measurements were to the right of this value, and a few measurements were to the left of this value. The resulting shape looks like a bell, and this is the shape that represents a normal distribution of data.
Now you should be able to complete the statement that was presented earlier in this lesson.
“The typical measurement of the diameter is approximately 9.4 inches, give or take 0.4 inches.”
This statement assumes that the mean of the measurements was 9.4 inches and the standard deviation of the measurements was 0.4 inches. It also assumes that the standard deviation is the difference between the mean and the first tick mark to the left of the mean.
For each of the following graphs, complete the statement. Fill in the first blank in each statement with the mean and the second blank in each statement with the standard deviation. Assume that the standard deviation is the difference between the mean and the first tick mark to the left of the mean.
a) “The typical measurement is approximately ______ in the bank, give or take ______.”
“The typical measurement is approximately $500 in the bank, give or take $50.”
b) “The typical measurement is approximately ______ minutes played, give or take ______ minutes.”
“The typical measurement is approximately 64 minutes played, give or take 6 minutes.”
Points to Consider
- Is there a way to determine the actual values for a give or take statement?
- Can a give or take statement go beyond a single give or take?
- Can all the actual values be represented on a bell curve?