Chapter 1 Lesson 7 Variance and Standard Deviation

Vocabulary Deviation- Difference of each data value from the mean. Variance- Roughly the average of the squared deviation. Standard Deviation- The square root of the variance. Sample Variance (S 2 )- Dividing the sum of the squared deviations of the data from the mean by one less than the number of elements in the set. Population Variance (σ 2 )- Dividing the sum of the squared deviations of the data from the mean by the number of elements in the set.

Calculating the Variance and Standard Deviation 1) Calculate the mean of the data 2) Find the deviation (difference) of each value from the mean (value – mean) 3) Square each deviation and add the squares 4) Divide the sum of squared deviations by n-1, this is the variance 5) Take the square root of the variance, this is the standard deviation

Symbols

Positive or Negative?

Standard Deviation Smaller Standard Deviation = Numbers are close together Larger Standard Deviation = Numbers are spread out

Standard Deviation

Example Mean? Variance? Standard Deviation? HeightDeviationSquare of Deviation

Example Questions Variance is 25, What is the Standard Deviation? Standard Deviation is 4.5, What is Variance? Mean score is 35, Squared Deviation of a score is 49, What is the score? Mean score is 105, Score’s deviation is -27, What is the score?

Spread vs. Center Measures of Center Mean Median Measures of Spread Variance Range IQR Standard Deviation

Homework Worksheet 1-7

Chapter Review Progress Self Test Pages all

Chapter Test Handwritten/Hand-typed notes allowed No Book No Asking a Neighbor Don’t Do Problems 13-15