introductory statistics lesson 2.3 c objective:
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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. - PowerPoint PPT PresentationTRANSCRIPT
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