Statistics 11/29 Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? LESSON Standard Deviation shows the variation in data. If the data is close together, the standard deviation will be small. If the data is spread out, the standard deviation will be large. Standard Deviation is often denoted by the lowercase Greek letter sigma, . Mean is represented by and n is the number of items.

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? Analyzing the data: Consider both sets of scores. Both classes have the same mean, 76. However, each class does not have the same scores. Thus we use the standard deviation to show the variation in the scores. With a standard variation of 14.53 for the first class and 19.6 for the second class, what does this tell us?

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule?

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? Variance is the average squared deviation from the mean of a set of data. It is used to find the standard deviation. Variance = (Sx)2 or (o x)2

Find the variance and standard deviation Ex. The math test scores of five students are: 92,88,80,68 and 52. Ex. A different math class took the same test with these five test scores: 92,92,92,52,52.

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule?

Essential Question: How do you use the empirical rule? Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? Data Frequency 2 7 4 8 6 9

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? Empirical Rule (68-95-99.7%) For data with a (symmetric) bell-shaped distribution, the standard deviation has the following characteristics. About 68% of the data lie within one standard deviation of the mean. About 95% of the data lie within two standard deviations of the mean. About 99.7% of the data lie within three standard deviation of the mean.

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? The bell curve which represents a normal distribution of data shows what standard deviation represents. One standard deviation away from the mean ( ) in either direction on the horizontal axis accounts for around 68 percent of the data. Two standard deviations away from the mean accounts for roughly 95 percent of the data with three standard deviations representing about 99 percent of the data.

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule?

Using the Empirical Rule Example: The mean value of homes on a street is $125 thousand with a standard deviation of $5 thousand. The data set has a bell shaped distribution. Estimate the percent of homes between $120 and $130 thousand. μ – σ μ μ + σ ____% of the houses have a value between $120 and $130 thousand.

Using the Empirical Rule Example: The mean value of homes on a street is $125 thousand with a standard deviation of $5 thousand. The data set has a bell shaped distribution. Estimate the percent of homes between $120 and $130 thousand. μ – σ μ μ + σ ____% of the houses have a value between $120 and $130 thousand.

Objective: Students will be able to find standard deviation and variance. Standards: 1.02 Summarize and analyze univariate data to solve problems Essential Question: How do you use the empirical rule? Ex. A normal distribution has a mean of 11 and a standard deviation of 3. What percent of values are from 11 to 20?