Lesson 1-1 Name:______
Collecting Data
FST - Notes Date:______
Objectives
Use sampling and the capture-recapture method to make estimations about a population.
Analyze, interpret and evaluate data for its validity.
Book Notes - Vocabulary
Statistics
Data (qualitative vs. quantitative)
Variable
Population
Sample
Random
Bias
Capture Recapture Method
Class Notes
Examples
Reading Data
Use this table from The Statistical Abstract of the United States 1990
Travel by U. S. Residents by Selected Trip Characteristics: 1983 to 1988 (in Millions)
Characteristic / Trips / Person-Trips11983 / 1984 / 1985 / 1986 / 1987 / 1988 / 1983 / 1984 / 1985 / 1986 / 1987 / 1988
Total / 540.9 / 528.2 / 558.4 / 592.3 / 636.3 / 656.1 / 1057.8 / 1012.0 / 1077.6 / 1121.5 / 1191.1 / 1232.5
Purpose
Visit friends
and relatives / 181.9 / 180.5 / 206.8 / 214.9 / 210.5 / 213.8 / 384.6 / 384.6 / 430.8 / 442.5 / 437.1 / 425.8
Other Pleasure / 189.6 / 170.5 / 177.6 / 200.3 / 234.4 / 241.5 / 401.4 / 349.7 / 376.0 / 418.9 / 464.6 / 502.1
Business or
convention / 103.6 / 114.5 / 1333 / 140.0 / 157.5 / 155.6 / 146.4 / 15301 / 185.2 / 189.0 / 206.2 / 211.7
Other / 65.8 / 62.7 / 40.7 / 37.1 / 33.9 / 45.1 / 125.4 / 121.6 / 85.6 / 71.1 / 83.2 / 92.9
Mode of transport
Auto, truck,
recreation
vehicle / 396.1 / 380.9 / 376.1 / 405.6 / 433.7 / 472.6 / 839.8 / 794.0 / 797.7 / 832.1 / 889.4 / 952.2
Airplane / 116.2 / 118.8 / 140.5 / 143.4 / 160.7 / 154.6 / 174.2 / 174.5 / 217.3 / 231.0 / 239.9 / 238.6
Other / 28.6 / 28.5 / 41.8 / 43.3 / 41.9 / 28.9 / 43.8 / 43.5 / 62.6 / 58.4 / 61.8 / 41.7
Vacation Trip / 307.8 / 333.3 / 339.8 / 354.3 / 366.2 / 396.2 / 642.3 / 689.8 / 728.7 / 752.4 / 775.2 / 830.9
Weekend Trip / 225.5 / 211.4 / 224.0 / 252.0 / 274.4 / 27127 / 485.0 / 424.9 / 470.1 / 513.5 / 559.4 / 560.0
1 A count of times each person (child or adult) goes on a trip.
Source: US Travel Data Center, Washington, DC, National Travel Survey, annual. (Copyright.)
1. Explain the information conveyed by the number 214.9 in the fourth column (1986) under Trips.
2. Which numbers in the fourth column total 592.3?
3. How many trips were taken by airplane in 1987?
4. How many people took trips by airplane in 1987??
Population, Sample, Variable, Bias, Random
For 1 and 2, identify the population, sample and the variable of interest
1. Before cleaning a sofa with a new cleaning solution, a man cleans a 5 cm by 5 cm section which is not visible.
2. In July 1990 the city of Chicago announced that it would set up roadside checkpoints to stop motorists at random in order to check for drunken drivers.
In 3 and 4 determine why a sample is used rather than a survey of the total population.
3. The Nielsen television rating service determines the U.S. television ratings with a sample of 1200 homes.
4. A Fireworks company tests some of the sparklers it manufactures.
Population problems (Capture-Recapture Method)
1. In order to estimate the number of blue gills in a small lake, a biologist captured and carefully tagged 85 of the fish. She then released them. One week later she caught 122 blue gills, of which 18 were tagged. About how many blue gills are in the lake?
2. In 1988 it was estimated that about 6.5 million Ghanaians could read English. If the literacy rate was about 45% estimate the population of Ghana in 1988.
3. A group of people were trying to estimate the number of Great Northern beans in a one pound bag. They withdrew 50 beans and replaced them with pinto beans. They mixed the beans well. They withdrew 120 beans of which 4 were pinto beans. About how many Great Northern beans were in the original one-pound bag?
Homework pg 7-9
5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 19, 21-24
Lesson 1-2 Name:______
Tables and Graphs
FST - Notes Date:______
Objectives
Read and interpret bar graphs, circle graphs, coordinate graphs, stemplots, boxplots, and histograms.
Draw graphs to display data.
Notes
Bar graphs
Pie Charts (Circle Graphs)
What are some things to consider when looking at representations (eg. graphs, charts) of data?
1.
2.
3.
Can data always be trusted? Why/why not?
How would you display the following data? Create a display that you think best represents these data.
Examples
Reading Graphs
In 1-4, use the
following graph.
1. What was the total median family income for
all regions in 1988?
2. How did the total family income compare with
that for families in the South in 1988?
3. How did the median income for families with one
or two earners compare with the median income for
families with three or more earners in 1988?
4. True or False: Family income tended to be higher in
households with more than one earner.
In 5-7, use a pie chart at the right
from The Statistical Abstract of the
United Stated 1990.
5. What group suffered the most
deaths from AIDS from 1982
to 1988?
6. What age group had the least number of deaths
from AIDS from 1982 to 1988?
7. About how many people under the age of 30 died
from AIDS from 1982 to 1998?
Drawing Graphs
8. Advertising-Estimated Expenditures, by Selected Media (in Millions of Dollars)
1970 / 1980 / 1988Newspapers / 5704 / 14,794 / 31,197
Television / 3596 / 11,469 / 25,686
Radio / 1308 / 3702 / 7798
Direct Mail / 2766 / 7596 / 21,115
Source: Statistical Abstract of the United States 1990, table no. 934
Draw a bar graph to display the total amount spent on advertising in these media in 1970, 1980, and 1988.
9. The data below show how teenagers spend their money
Boys / Spending per Week / Girls / Spending per WeekFood, Snacks / $10.10 / Clothing / $10.65
Clothing / $6.19 / Food, Snacks / $6.50
Entertainment / $4.35 / Entertainment / $3.45
Music / $1.55 / Grooming / $3.35
Grooming / $1.10 / Music / $1.80
Source: Rand Youth Poll, Summer/Fall 1990.
Draw a circle graph to show how boys spend their money.
Homework pg 13-16: 1-5, 7, 10,11, 12a(bar graph) b(circle graph), 14, 16, 17, 19-21
Review
1. From several locations on an island, a naturalist catches 96 rabbits, tags them, and releases them. Ten days later 120 rabbits are caught and 36 have tags. Estimate the number of rabbits on the island.
2. In order to learn the TV Habits of all Carlton students, those students entering the north entrance of the school between 7:30 a.m. and 7:45 a.m. are asked which TV programs they watched last night. Identify the population, the sample, and the variable of interest.
Lesson 1-3 Name:______
Other Displays
FST - Notes Date:______
Objectives
Read and interpret bar graphs, circle graphs, coordinate graphs, stemplots, boxplots, and histograms.
Draw graphs to display data.
Definitions and terms
Scatterplot
Line Graph
Average Rate of Change
(Include Formula)
Increasing Interval
Decreasing Interval
Constant Interval
Stem-and-leaf diagram (Stemplot)
Maximum
Minimum
Range of data
Outliers
Back-to-Back Stemplot
Univariate Data vs. Bivariate Data
Examples
For 1-4 use the stemplot below
3rd Period / 6th Period2 / 5
3 / 7 9
0 / 4
6 3 0 / 5 / 5 5 6
9 / 6 / 0 1 2 2
2 1 0 0 / 7 / 0 1 1 3 4 5
6 4 2 1 1 0 / 8 / 3 4 7 7
9 8 5 5 4 3 / 9 / 1 6
0 0 / 10
1. Identify the a. minimum, b. maximum, and c. range for both periods.
2. How many students in each class took the test?
3. How many students in each class scored in the 70’s?
4. Which scores (if any) appear to be outliers in each class?
In 5-8 use the graph below of a science experiment. Acrylic acid was frozen in a test tube containing a thermometer. Later the test tube was placed in a beaker of warm water in which a second thermometer had been placed. Temperature readings were taken on both thermometers over a period of time. These data were plotted on the graph.
5. At what time was the water temperature 30oC?
6. What was the initial temperature of the acrylic acid?
7. What was the range of temperature for the water?
8. Calculate the average rate of change of the water temperature over the first 40 minutes.
Why is the result negative?
9. Use the data below for monthly normal temperatures in degrees Fahrenheit for Nashville, TN and Seattle, WA. Draw a line graph.
Jan. / Feb. / Mar. / Apr. / May / JuneNashville / 37 / 40 / 49 / 60 / 68 / 76
Seattle / 39 / 43 / 44 / 49 / 55 / 60
Source: The World Almanac and Book of Facts 1989
10. Theresa Chair gave her FST classes a test on Chapter 1. the 4th period scores were
68 86 65 88 76 86 43 91
42 86 79 82 85 72 20 100
The 8th period scores were:
78 96 89 85 86 86 52 90
53 97 100 89 89 97 85
Make a back-to-back stemplot of these data.
Review
In Pepin county 5% of the residents (at least 10 years old) are illiterate. There are 85,450 people who can read in the county. What is the population of Pepin county.
Homework pg 20-23:
1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20
Lesson 1-4 Name:______
Measures of Center
FST - Notes Date:______
Objectives
· Calculate the measures of center and measures of spread for a data set.
· Use ∑-notation to represent a sum, mean, variance, and standard deviation.
· Use statistics to describe and compare data sets.
Terms and Definitions
Summation Notation
Index Subscript
Measures of Center (Central Tendency)
Mean (Include notation and formula)
Median (Include a comparison when there is an even number of data versus an odd number)
Mode
Class Notes
Examples
1. Of the central measures, which one(s) can be numbers that are not in the data set?
When calculating measures of central tendency, which one(s) can have:
no answer? more than one answer?
Do the mean, median, and mode have units?
Which central measure(s) of typical data require the data to be in numerical order from smallest to largest?
Mathematics Class Enrollment0 / 9
1 / 2 / 4 / 4 / 5 / 7 / 8 / 9
2 / 0 / 4 / 6 / 6 / 7 / 7 / 7 / 8 / 9 / 9
3 / 2 / 3 / 3 / 6
2. Use the stemplot
at the right. Find
a. the mean, b. the
median, and c. the
mode.
3. Jerry Attic was a dedicated golfer. His scores over a two month period were 93, 85, 85, 103, 97, 87, 88, 86, 94, 99, 101, 85, and 89. What would Jerry have to shoot in his next game to lower his mean score to 90?
4. In an algebra class of 24 students the mean grade on a test was 82; in another algebra class with 30 students the mean was 74. What was the combined mean of the two classes?
Suppose that xi equals the number of loaves of bread sold in the ith day by the corner grocery store.
x1 = 15, x2 = 30, x3 = 29, x4 = 24, x5 = 31, x6 = 12
5. Find
6. Write an expression using sigma (summation notation) which indicates the total number of loaves of bread.
7. Write an expression using summation notation which indicates the mean number of loaves of bread sold daily.
8. Calculate the following
a. b. c.
9. The weekly salaries of workers in a small factory are $250, $250, $375, $400, $400, $400, $400, $425, $500, and $900. If the top salary is increased to $1000, how will that affect the
a. mean? b. median?
10. If data values are bunched close together, then ______is probably
the best measure of center. Outliers will have less effect on ______
or the middle data.
Homework pg 27-30: 5, 6, 9-12,14, 16-18, 21, 22, 24
Lesson 1-5 Name:______
Quartiles, Percentiles, and Box Plots
FST - Notes Date:______
Book Notes
Rank-Ordered
Quartiles
Second Quartile (Middle)
First Quartile (Lower)
Third Quartile (upper)
Interquartile Range / IQR
Five Number Summary
Box Plot
Percentile
Class Notes
Suppose that we measure the heights in inches of the players on a baseball team.
There heights in inches are
86 70 68 71 61 63 62 60 64
Below is the data of heights of children in a small elementary class.
The units are in centimeters
63, 79, 84, 84, 87, 88, 90, 95, 97, 102
The child with the height of 95 cm is at what percentile?
The child with the height of 84 cm is at what percentile?
Which child is at the 40th percentile?
Which child that is at least at the 75th percentile?
Examples
1. Consider the following data concerning mathematics class enrollment at one school
Mathematics Class Enrollment0 / 9
1 / 2 / 4 / 4 / 5 / 7 / 8 / 9 / 9
2 / 0 / 4 / 6 / 6 / 7 / 7 / 7 / 7 / 7 / 8 / 8 / 9
3 / 2 / 3 / 3 / 6
a. Find the median
b. Find the first quartile
c. Find the third quartile
d. Find the interquartile range
2. Draw the box-plot that represents the data.
3. Determine if there are any outliers and adjust your plot according to your findings.
4. What is the class enrollment at the
a. 12th percntile?
b. 80th percentile?