2. 3.3 Working with Grouped Data Objectives: By the end of this section, I will be able to… 1) Calculate the weighted mean. 2) Estimate the mean for grouped data. 3) Estimate the variance and standard deviation for grouped data.

3. Weighted Mean Shania has the following GRADES in her Statistics class: 87% Tests 74% Quizzes 91% Homework 92% Labs 85% Participation Her teacher uses the following WEIGHTS for grades: Tests 35% Quizzes 25% Homework 20% Labs 10% Participation 10% What is Shania’s Mean for her class? Multiply 0.305 0.185 0.182 0.092 0.085 0.305 + 0.185 + 0.182 + 0.092 + 0.085 = 0.849 or 84.9%

5. Finding the mean, median, and mode of a distribution Interval 0 – 9 10 – 19 20 – 29 30 – 39 40 – 49 Class Midpoint 4.5 14.5 24.5 34.5 44.5 Frequency mf mf AMOUNT OF MONEY YOU SPENT ON GAS IN ANY GIVEN WEEK MEAN = SUM of this column/n MEDIAN = interval with the middle number, you must cut the frequency in half and find in which interval it would be located MODE = interval with the highest frequency

6. Variance and Standard Deviation of Grouped Data 1.Variance 2.Standard Deviation m = the class midpoints n = total number of items

7. Finding the variance and standard deviation of a distribution Interval 0 – 9 10 – 19 20 – 29 30 – 39 40 – 49 m 4.5 14.5 24.5 34.5 44.5 f AMOUNT OF MONEY YOU SPENT ON GAS IN ANY GIVEN WEEK mf Variance = Sum of column / n

8. Try on Calculator Find the estimated mean, variance, and standard deviation using your calculator. Use the class midpoint as your “x” value in your L1.