Section 2.4: Measures of Spread

Example: Using the number of days of vacation for 6 students, find the range, variance and standard deviation. (this is a sample) Data set: x

Using your calculator for finding the variance and standard deviation. 68 – 95 – 99.7 Rule (Empirical Rule) If the data are distributed normally, then approximately 68% of all observations lie within 1 standard deviation from the mean; 95% of all observations lie within 2 standard deviations from the mean; 99.7% of all observations lie within 3 standard deviations from the mean,

Example: Let X = test scores and assume that the test scores are distributed normal with a mean of 80 and a standard deviation of 6. Answer the following questions: a.New Notation: b.Draw a sketch of this distribution and label the x-axis.

c. Find the area between 74 and 86. d. Find the area between 68 and 92. e. Find the area between 62 and 98. f. Find the area greater than 86.

g. Find the area less than 68. h. Find the area greater than 98. i. Find the area between 80 and 86. j. Find the area between 68 and 74.

k. Find the area between 68 and 86. l. If a class has 40 students in it, how many scored between 74 and 86? m. If a class has 40 students in it, how many scored between 74 and 92?

An outlier will be defined as any observation that lie more than 2 standard deviations away from the mean. Ex. Given the normal distribution with a mean of 135 pounds and a standard deviation of 25 pounds, is the observation of 144 pounds an outlier? Is the observation of 71 pounds an outlier?