introductory statistics lesson 2.3 c objective:

Introductory Statistics

Lesson 2.3 C

Objective:

SSBAT find the mean of a frequency distribution.

Standards: M11.E.2.1.1

Mean of a Frequency Distribution

=

Where: x is the midpoint of a class and

f is the frequency of that class

Mean of a Frequency Distribution (in words)

1. Find the Midpoint of each class

2. Multiply the midpoint of each row and its frequency together

3. Add all of the products together from step 2

4. Add all the individual frequencies together (Σf)

5. Divide the answer from Step 3 by the answer from step 4

Example 1

The heights (in inches) of 18 female students in a physical education class are listed in the frequency distribution below. Find the mean of the distribution.

Heights Frequency

60 – 62 4

63 – 65 5

66 – 68 8

69 – 71 1

1st: Find the Midpoint of each class

=

Example 1 continued

1st: Find the midpoint of each class

Heights Frequency Midpoint

60 – 62 4 61

63 – 65 5 64

66 – 68 8 67

69 – 71 1 70

2nd: Find (x · f) Frequency times Midpoint

Example 1 continued

2nd: Find (x · f)

Heights Frequency Midpoint x · f

60 – 62 4 61 244

63 – 65 5 64 320

66 – 68 8 67 536

69 – 71 1 70 70

3rd: Find Σf and Σ (x·f)

Example 1 continued

3rd: Find Σf and Σ (x·f)

Heights Frequency Midpoint x · f

60 – 62 4 61 244

63 – 65 5 64 320

66 – 68 8 67 536

69 – 71 1 70 70

n = Σf = 18 Σ(x · f) = 1170

4th: Divide Σ(x · f) by

Example 1 continued

=

= 65

Example 2

Use the frequency distribution below to find the mean number of minutes that a sample of Internet subscribers spent online during their most recent session.

Number of Minutes

Frequency f

7 – 18 6

19 – 30 10

31 – 42 13

43 – 54 8

55 – 66 5

67 – 78 6

79 – 90 2

=

Class Midpoint, x

12.5

24.5

36.5

48.5

60.5

72.5

84.5

xf

75

245

474.5

388

302.5

435

169

208950

Example 2 continued.

=

= 41.78

3. The frequency distribution shows the number of touchdowns scored by team during a season. Find the Mean of the Distribution.

Class Frequency15 – 24 1625 – 34 3435 – 44 3045 – 54 2355 – 64 1365 – 74 2

Class Frequency Midpoint15 – 24 16  25 – 34 34  35 – 44 30  45 – 54 23  55 – 64 13   65 – 74 2  

3. Continued.

19.5

29.5

39.5

49.5

59.5

69.5

Class Frequency Midpoint x · f15 – 24 16  19.525 – 34 34  29.535 – 44 30  39.545 – 54 23  49.555 – 64 13  59.5 65 – 74 2  69.5

3. Continued.

312

1003

1185

1138.5

773.5

139

4551 n = 118

3. Continued.

=

= 38.57

Homework

Worksheet 2.3 C