3.3 Working with Grouped DataObjectives:By the end of this section, I will beable to…

1) Calculate the weighted mean.

2) Estimate the mean for grouped data.

3) Estimate the variance and standard deviation for grouped data.

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

Multiply

Multiply

Multiply

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%

• Symbol for mean of grouped data:

• We can’t use since we are ESTIMATING!

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

m f 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

Variance and Standard Deviation of Grouped Data

1. Variance

2. Standard Deviation

• m = the class midpoints• n = total number of items

•  

•  

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

m - (m - )2 (m - )2 ∙ fmf

Variance = Sum of column /

n

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.