Normal Distribution Warm Up # 5 on iPads Write answers on index card Statistics: Normal Distribution Warm Up # 5 on iPads Write answers on index card

Essential Question: What is true about normally distributed data?

Compare and Contrast: 1 0 2 5 6 7 8 9 2 2 5 8 9 9 3 4 3 7 5 2 5 6 6 1 2 5 7 8 1 0 2 2 2 5 8 3 4 5 6 7 8 9 4 3 7 5 6 5 2 5 6 1 2 2 5 3 4 5 4 3 7 8 8 9 5 2 5 6 6 7 8 9 6 1 2 5 7 8 9 9

Shapes of Histograms… Symmetry A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size: Frequency Variable Frequency

Shapes of Histograms… Skewness A skewed histogram is one with a long tail extending to either the right or the left: Frequency Variable Positively Skewed Negatively Skewed (Skewed right) (Skewed left)

Mean vs. Median The mean and the median are the most common measures of center. If a distribution is perfectly symmetric, the mean and the median are the same. The mean is not resistant to outliers. You must decide which number is the most appropriate description of the center... MeanMedian Applet

Normal Distribution: Frequency distribution that often occur when there is a large number of values in a set of data Symmetric bell-curved shape which is called a normal curved Concentrated around the center portion of distribution Mean = median = mode Small standard deviation

Normal Distribution: What percent of the data would you expect in each region of the normal distribution curve?

How to draw a normal distribution curve? Example 1: The average healing time of a certain type of incision is 240 hours within the standard deviation of 20 hours. Sketch a normal curve. Step1: Find the number that is + or minus 1, 2, and 3 standard deviation from the mean. Step 2: Draw the curve.

Example 2: Refer to the past example. Suppose a hospital has treated 2000 patients in the past five years having this type of incision. Estimate how many patient heal during these intervals: 220 -260 hours 200 – 280 hours 180 – 300 hours

Another Example: The lifetime of 10,000 watch batteries are normally distributed. If the mean lifetime is 500 days and the standard deviation is 60 days, sketch a normally distributed curve. What percentage of the batteries would last more than 500 days? How many batteries would last more than 500 days? What percentage of batteries would last between 380 and 560 days? How many batteries would last between 380 and 560 days?

Now you try: The scores of 500 freshman taking Psychology 101 had an arithmetic mean of 60 with a standard deviation of 10. Sketch the curve (assume that the data is normally distributed)

From the previous example: Determine what percent and how many fit the following criteria: Scores of 50 to 70 Scores of 40 to 80 Scores of 30 to 90 Scores of more than 60 Scores of less than 30 Scores of less than 60

Teacher Curve:

Create a “teacher curve for the 500 freshman taking Psychology 101. How many A’s, B’s, C’s, D’s and F’s are there?

Revisiting the EQ: What is true about normally distributed data?

Homework: