Aim: Measures of Dispersion
MR2 Lesson #42
Aim:
Measures of Dispersion
Do Now: The table displays the frequency of scores on a twenty point quiz. The mean of the quiz scores is 18. Find the value of k in the table.
Answer: 11
Measures of Dispersion The measure of dispersion is a number that indicates the spread or variation of data values about the mean. Some of the measures of dispersion are: • Range • Variance • Standard Deviation
Range: The simplest of our methods for measuring dispersion is range. Range is the difference between the largest value and the smallest value in the data set. Example 1: Find the range of the following set of data
MR2 Lesson #42
Variance
Use THIS one!!!!!!!!
Standard Deviation SD=√Variance
V=SD2
Use THIS one!!!!!!!!
MR2 Lesson #42
0
1. Which of the following sets of data has the greatest range? (1) 32, 65, 34, 43, 16 (3) 65, 54, 75, 45, 86 (2) 14, 76, 56, 42, 86 (4) 21, 45, 90, 65, 54 2. In Math 101 at a local college, the youngest member of the class was 18 and the oldest member was 43. What is the range in ages? 3. If the variance of a set of data is 16, what is the standard deviation? (1) 256 (2) 32 (3) 8 (4) 4 4. If the standard deviation of a set of data is 16, what is the variance? (1) 256 (2) 32 (3) 8 (4) 4
MR2 Lesson #42 Find the standard deviation, to the nearest tenth, for the following data: 4, 9, 8, 10, 11, 10, 13, 13, 12, 12, 15, 12, 16, 16
Population Standard Deviation -- this is what we use!!
Example In Australia, a study of farms with 30 or fewer sheep produced the following data.
What is the mean for the number of sheep per farm? Find the standard deviation to the nearest tenth. What is the total number of farms that lie within one standard deviation of the mean?
MR2 Lesson #42
Homework 1. Mel took 12 tests in Sequential Math III and received the following grades: 85, 89, 89, 89, 90, 90, 90, 92, 92, 96, 96, 100
Find, to the nearest tenth, the standard deviation. What percent of the test grades are more than one standard deviation above the mean?
2.
3.
An electronics company produces a headphone set that can be adjusted to accommodate different-sized heads. Research into the distance between the top of people’s heads and the top of their ears produced the following data, in inches: 4.5, 4.8, 6.2, 5.5, 5.6, 5.4, 5.8, 6.0, 5.8, 6.2, 4.6, 5.0, 5.4, 5.8 The company decides to design their headphones to accommodate three standard deviations from the mean. Find, to the nearest tenth, the mean, the standard deviation, and the range of distances that must be accommodated.
Mr. Koziol has 17 students in his high school golf club. Each student played one round of golf. The summarized scores of the students are listed in the accompanying table.
Find the population standard deviation of this set of students' scores, to the nearest tenth. How many of the individual students' golf scores fall within one population standard deviation of the mean?
Aim:
Measures of Dispersion
Do Now: The table displays the frequency of scores on a twenty point quiz. The mean of the quiz scores is 18. Find the value of k in the table.
Answer: 11
Measures of Dispersion The measure of dispersion is a number that indicates the spread or variation of data values about the mean. Some of the measures of dispersion are: • Range • Variance • Standard Deviation
Range: The simplest of our methods for measuring dispersion is range. Range is the difference between the largest value and the smallest value in the data set. Example 1: Find the range of the following set of data
MR2 Lesson #42
Variance
Use THIS one!!!!!!!!
Standard Deviation SD=√Variance
V=SD2
Use THIS one!!!!!!!!
MR2 Lesson #42
0
1. Which of the following sets of data has the greatest range? (1) 32, 65, 34, 43, 16 (3) 65, 54, 75, 45, 86 (2) 14, 76, 56, 42, 86 (4) 21, 45, 90, 65, 54 2. In Math 101 at a local college, the youngest member of the class was 18 and the oldest member was 43. What is the range in ages? 3. If the variance of a set of data is 16, what is the standard deviation? (1) 256 (2) 32 (3) 8 (4) 4 4. If the standard deviation of a set of data is 16, what is the variance? (1) 256 (2) 32 (3) 8 (4) 4
MR2 Lesson #42 Find the standard deviation, to the nearest tenth, for the following data: 4, 9, 8, 10, 11, 10, 13, 13, 12, 12, 15, 12, 16, 16
Population Standard Deviation -- this is what we use!!
Example In Australia, a study of farms with 30 or fewer sheep produced the following data.
What is the mean for the number of sheep per farm? Find the standard deviation to the nearest tenth. What is the total number of farms that lie within one standard deviation of the mean?
MR2 Lesson #42
Homework 1. Mel took 12 tests in Sequential Math III and received the following grades: 85, 89, 89, 89, 90, 90, 90, 92, 92, 96, 96, 100
Find, to the nearest tenth, the standard deviation. What percent of the test grades are more than one standard deviation above the mean?
2.
3.
An electronics company produces a headphone set that can be adjusted to accommodate different-sized heads. Research into the distance between the top of people’s heads and the top of their ears produced the following data, in inches: 4.5, 4.8, 6.2, 5.5, 5.6, 5.4, 5.8, 6.0, 5.8, 6.2, 4.6, 5.0, 5.4, 5.8 The company decides to design their headphones to accommodate three standard deviations from the mean. Find, to the nearest tenth, the mean, the standard deviation, and the range of distances that must be accommodated.
Mr. Koziol has 17 students in his high school golf club. Each student played one round of golf. The summarized scores of the students are listed in the accompanying table.
Find the population standard deviation of this set of students' scores, to the nearest tenth. How many of the individual students' golf scores fall within one population standard deviation of the mean?
