- Understand the meaning of normal distribution and bell-shape.
- Estimate the mean and the standard deviation of a normal distribution.
The diameter of a circle is the length of the line through the center and touching two points on the circumference of the circle.
If you had a ruler, you could easily measure the length of this line. However, if your teacher gave you a golf ball and asked you to use a ruler to measure its diameter, you would have to create your own method of measuring its diameter.
Using your ruler and the method that you have created, make two measurements of the diameter of the golf ball (to the nearest tenth of an inch). Your teacher will prepare a chart for the class to create a dot plot of all the measurements. Can you describe the shape of the plot? Do the dots seem to be clustered around one spot (value) on the chart? Do some dots seem to be far away from the clustered dots? After you have answered these questions, pick two 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.
You have probably noticed that the measurements of the diameter of the golf ball 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 1.6 inches, with a few measurements to the right of this value and a few measurements to the left of this value. The resulting shape looks like a bell and is the shape that represents the normal distribution of the data.
Approximately 68% of all the data is located between these inflection points.
For now, that is all you have to know about standard deviation. It is the spread of the data away from the mean. In the next lesson, you will learn more about this topic.
Now you should be able to complete the statement that was given in the introduction.
For each of the following graphs, complete the statement “The typical measurement is approximately ______ give or take ______.”
In this lesson you learned what was meant by the bell curve and how data is displayed on this shape. You also learned that when data is plotted on the bell curve, you can estimate the mean of the data with a give or take statement.
Points to Consider
- Is there a way to determine actual values for the give or take statements?
- Can the give or take statement go beyond a single give or take?
- Can all the actual values be represented on a bell curve?