http://www.ck12.org Chapter 6. Normal Distribution Curves
In a normal distribution, on either side of the line of symmetry, the curve appears to change its shape from being
concave down (looking like an upside-down bowl) to being concave up (looking like a right-side-up bowl). Where
this happens is called aninflection pointof the curve. If a vertical line is drawn from an inflection point to the
x-axis, the difference between where the line of symmetry goes through thex-axis and where this line goes through
thex-axis represents 1 standard deviation away from the mean. Approximately 68% of all the data is located within
1 standard deviation of the mean.
To emphasize this fact and the fact that the mean is the middle of the distribution, let’s play a game of Simon Says.
Using color paper and 2 types of shapes, arrange the pattern of the shapes on the floor as shown below. Randomly
select 7 students from your class to play the game. You will be Simon, and you are to give orders to the selected
students. Only whenSimon Saysare the students to obey the given order. The orders can be given in many ways,
but 1 suggestion is to deliver the following orders:
- “Simon Says for Frank to stand on the rectangle.”
- “Simon Says for Joey to stand on the closest oval to the right of Frank.”
- “Simon Says for Liam to stand on the closest oval to the left of Frank.”
- “Simon Says for Mark to stand on the farthest oval to the right of Frank.”
- “Simon Says for Juan to stand on the farthest oval to the left of Frank.”
- “Simon Says for Jacob to stand on the middle oval to the right of Frank.”
- “Simon Says for Sean to stand on the middle oval to the left of Frank.”
Once the students are standing in the correct places, pose questions about their positions with respect to Frank. The
members of the class who are not playing the game should be asked to respond to these questions about the position
of their classmates. Some questions that should be asked are the following:
- “Which 2 students are standing closest to Frank?”
- “Are Joey and Liam both the same distance away from Frank?”
- “Which 2 students are furthest away from Frank?”
- “Are Mark and Juan both the same distance away from Frank?”
When the students have completed playing Simon Says, they should have an understanding of the concept that the
mean is the middle of the distribution and the remainder of the distribution is evenly spread out on either side of the
mean.
The picture below is a simplified form of the game you have just played. The yellow rectangle is the mean, and the
remaining rectangles represent 3 steps to the right of the mean and 3 steps to the left of the mean.