Download Chapter 3 Notes - Clinton Public Schools

Chapter 3 Notes
Name: _____________________________________________________ Period: ______
Measures of Center
Arithmetic mean (or just mean)
Sample Mean
Population Mean
The mean ALWAYS has one more decimal place than the original data.
WEIGHTED MEAN:
1. The syllabus in Statistics class states that the final grade each 9 weeks is determined by tests
(45%), quizzes (20%), homework/classwork (10%), and Final Exam (25%). Calculate the final grade
using the following individual means.
Tests: 83
Quizzes: 90
Homework: 98 Final Exam: 87
2. GPA is figured by awarding each A 4 points, each B 3 points, each C 2 points, each D 1 point, and
each F 0 points. Calculate the GPA of a student with 4 A’s, 9 B’s, 11 C’s, 4 D’s and 2 F’s.
Median:
3. If the data has an ODD number of values, the median is
_________________________________________________________________________________________________
4. If the data has an EVEN number of values, the median is
_________________________________________________________________________________________________
5. Does the median have to be in the data set? ______________________
Mode:
No Mode
Unimodal
Bimodal
Find the mode(s) and state the type.
6. 6, 4, 6, 1, 7, 8, 7, 2, 5, 7
7. 3, 4, 7, 8, 1, 6, 9
Multimodal
8. 2, 5, 7, 2, 8, 7, 9, 3
Choose an Appropriate Measure of Center – Remember…
Mode is used for qualitative data
Median is used for quantitative data when there are outliers OR data is skewed
Mean is used for quantitative data when there are no outliers AND data isn’t skewed
9. The average T-shirt size of American women.
10. The average salary for a professional team of baseball players.
11. The average price of homes in a subdivision of similar homes.
Graphs and Measures of Center
Mode: highest peak of a graph
Median- Divides the data in half
Means – pulled toward outliers – toward skew
12.
13.
14.
Measures of Dispersion
Range:
Variation: Deviation from the mean
Population Variance
Sample Variance
Standard Deviation:
Population Standard Deviation
Sample Standard Deviation
Use the Calculator to find the standard deviation and variance of both the SAMPLE and the
POPULATION. Like the MEAN, standard deviation and variance should be one more decimal place
than the data.
15. 12, 17, 13, 20, 13, 15, 16, 21, 27, 29, 25
Coefficient of Variation: Used to compare the spread of data from 2 different sources
The larger the percent the greater the spread.
16. Which set of data is more precise?
A. Test scores (out of 100): 97, 75, 93, 82, 79, 69, 73, 86, 96, 60, 72, 89
B. Quiz scores (out of 25): 19, 17, 18, 20, 25, 16, 9, 21, 24, 10, 8
Grouped Data- from a frequency distribution use the midpoint as the x value and the frequency
17. Find the standard deviation and variance of the following sample data.
Grade
Frequency
Midpoint
66-72
5
73-79
8
80-86
12
87-93
7
94-100
4
18. Find the standard deviation and variance of the following population data.
Gas Prices
2.95 – 2.99
3.00 – 3.04
3.05 – 3.09
3.10 – 3.14
3.15 – 3.19
3.20 – 3.24
Frequency
100
313
567
612
299
118
Midpoint
EMPIRICAL RULE: When data is symmetrical, the following is true
68% of data lies within : __________________________________________
95% of data lies within: ___________________________________________
99.7% of data lies within: _________________________________________
The average weight of newborn babies is symmetrical with a mean of 3325 grams and a standard
deviation of 571 grams.
19. What percentage of newborn babies weigh between 2183 and 4467 grams?
20. What percentage of newborn babies weight less than 3896 grams?
CHEBYSHEV’S THEOREM: When data is NOT symmetrical, the following is true
AT least 75% of data lies within _________________________________________
AT least 88.9% of data lies within ____________________________________
21. Suppose that in one small town, the average income is $34, 200 with a standard deviation of
$2200. What percentage of households earn between $29,800 and $36,500?
Decide if each statement is true or false.
22. If the standard deviation of a data set is zero, then all entries in the data set are equal to zero.
23. The population variance and sample variance are the same value for the same set of data.
24. It is possible to have a standard deviation of -3 for some data set.
25. It is possible to have a standard deviation of 435, 000 for some data set.
Use the empirical rule or Chebyshev’s Theorem to answer the following questions
26. Suppose that starting salaries for graduates of one university have a bell-shaped distribution with
a mean of $25,400 and a standard deviation of $1300. What percentage of graduates have starting
salaries between $22,800 and $28,000?
27. Suppose that electric bills for the month of May in one city have a symmetrical distribution with a
mean 119 units and a standard deviation of 22 units. What percentage of electric bills are less than
163 units?
28. Suppose that salaries for associate mathematics professors at one university have a mean of
$64,900 with a standard deviation of $9400. What is the minimum percentage of associate
professors with starting salaries between $46,100 and $83,700?
MEASURES OF RELATIVE POSITION
QUARTILES: data divided into 4 parts
Q1
Q2
Q3
5 Number summary on the calculator
PERCENTILES: data divided into 100 parts
When using this formula to find the location of the percentile’s value in the data set, you MUST make
sure that you remember 2 hints:
The formula solve for LOCATION – not the value itself
If the LOCATION is a decimal, you ALWAYS round up
Use the following data set of a class of 25 students’ ACT scores.
14
16
17
18
18
18
19
19
21
23
24
24
27
27
28
29
35
19
30
20
31
20
33
21
33
29. What value is the 10th percentile?
30. What value is the 40th percentile?
31. What value is the 98th percentile?
32. What percentile is the value of 23?
33. What percentile is the value of 35?
34. WHY can’t you score in the 100 percentile?
STANDARD SCORE: ***** This is the most important concept in Statistics
Also called the ________________ tells how many standard deviations it is from the mean.
Population:
Sample:
35. If the average score on the math section of the SAT test is 500 with a standard deviation of 150
points, what is the z score for a student who scored a 630?
36. Jodi scored an 87 on her Calculus test and was bragging to her best friend how well she had done.
She said that her class had an average of 80 with a standard deviation of 5; therefore she had done
better than the class average. Her best friend, Ashley, was disappointed. She has scored an 92 on her
test. The class average for her class was a 72 with a standard deviation of 6. Who really did better on
the test in respect to their class?
37. Carlita scored a 32 on her ACT and a 2130 on her SAT. Given the average ACT score is 18 with a
standard deviation of 6 and the SAT has an average of 1500 with a standard deviation of 150, which
exam did Carlita perform better on?
38. Don played in a local golf tournament for Charity and scores a round of 63 while the average
round for the day was 74 with a standard deviation of 3 strokes. Later that week, Don played in a
pro-am tournament and scored a 65 while the average score for the day was 79 with a standard
deviation of 4 strokes. Which was Don’s better round of golf in comparison to the competition?
(remember that in golf, lower scores are better)