Download STATS HOMEWORK

STATS HOMEWORK
Homework A: Reflection
What do you think of when you hear the word Statistics? Write a short paragraph
(6 sentence min.) answering the reflection question. Include what you are expecting to learn
in this topic and what you hope you will be able to do by the end of the topic.
Date due _______ Handed in: __
Homework B: Penny weight
Ask a question:
How much does a penny weigh?
Collect appropriate data:
We used a metric scale to weigh 32 pennies to the nearest centigram (1/100 of a gram). Here
are the resulting weights:
3.08, 2.50, 2.46, 3.05, 2.45, 3.12, 3.05, 3.14, 2.48, 3.10, 3.02, 2.47, 3.10, 3.03, 3.11, 2.52,
3.00, 3.09, 3.15, 3.06, 3.18, 2.42, 2.43, 2.50, 3.07, 3.09, 3.00, 3.09, 2.47, 3.05, 2.52, 3.07
a. The 32 measurements are not all the same. What is the source of this variation?
b. What do you think would happen if you weighed the same penny 32 times? How would you
expect that data to compare to the weights of the 32 different pennies?
c. Based on the data in Problem B4, how much would you expect the 33rd penny to weigh?
Could you be sure of its weight before weighing it? If you can’t name an exact weight, Could
you be confident about a range of weights that it falls between? Why?
Date due _______ Handed in: __
Homework C:
Investigation 2: How long is a minute?
Ask a question:
How good is your sense of time? How well can you judge the actual length of a minute
without a timing device? Are some people better at judging elapsed time?
Collect appropriate data:
Record in seconds the actual length of time a person judges to be a minute.
Will the data be qualitative or quantitative? Discrete or continuous?
Analyze the data:
What would a more useful graphical representation of the data look like?
a. How many of the estimates are between 33 and 89 seconds (inclusive)?
b. How many of the estimates are between 52 and 68 seconds (inclusive)?
Since the goal is to estimate when a minute has elapsed, it makes sense to consider how
close the estimates are to the correct response, which is 60 seconds.
a. How many people’s estimates were more than five seconds away from one minute?
(That is, how many of the responses were less than 55 seconds or greater than 65)
b. How many estimates were within five seconds of one minute?
c. How many estimates were more than 10 seconds away from one minute?
d. How many estimates were within 10 seconds of one minute?
Interpret the results:
Use all of your data analysis to answer the question.
Date due _______ Handed in: __
Homework D: Histograms
Answer the following questions in complete sentences.
What advantages does a histogram have over a stem and leaf plot? What are the
disadvantages of a histogram?
Using only the histogram and grouped frequency table given, give two descriptive
statements that provide an answer to the question “How well do people judge when a
minute has elapsed?
a. According to the histogram and grouped frequency table, how many people’s
estimates were outside the interval from 50 to less than 70 seconds? That is, how
many estimates were less than 50 seconds or 70 seconds or more?
b. How many estimates were within the interval from 50 to less than 70 seconds?
c. How many estimates were outside the interval from 40 to less than 80 seconds?
d. In Problem A5, only nine people’s estimates were more than 10 seconds away from
one minute. Does your answer to question (a) of this problem imply that the people in
this group were not as good at estimating a minute’s time? If so, why? If not, how
could you make a fairer comparison between the two sets?
Date due _______ Handed in: __
Homework E: Practice displays
52 estimates collected in answer to the question “How long is a minute?”
79 67 72 75 64 82 55 56 58 66 60 59 63 75 66 57 72 57 62 57 67 53 67 59 61 60
57 61 60 53 30 50 42 39 68 89 67 65 86 39 54 93 52 55 72 56 65 89 33 52 60 70
For this set of data, create a stem and leaf plot, a grouped frequency table, histogram, and a
relative and cumulative frequency table. Use the information to answer the question: “How
well do people judge when a minute has elapsed?”
Date due _______ Handed in: __
Homework F: How many Hats should you order?
See Worksheet
Date due _______ Handed in: __
Homework G: Allocations
Here is a line plot corresponding to an allocation of 45 coins in 9 stacks:
From this line plot, we can see that there are 3 stacks containing exactly 5 coins each, and 1
stack containing 6 coins. The maximum number of coins in a stack is 8, and the minimum is 2.
Rearrange the nine dots to form a line plot with each of these requirements:
Form a line plot with a mean equal to 5 that has exactly 2 stacks of 5 coins.
1. Form a line plot with a mean equal to 5 but a median not equal to 5.
2. Form a line plot with a mean equal to 5 that has no 5-coin stacks.
3. Form a line plot with a mean equal to 5 that has two 5-coin stacks, 4 stacks with more
than 5 coins, and 3 stacks with fewer than 5 coins.
4. Form a line plot with a mean equal to 5 that has two 5-coin stacks, 5 stacks with more
than 5 coins, and 2 stacks with fewer than 5 coins.
5. Form a line plot with a mean equal to 5 that has two 5-coin stacks, two 10-coin stacks,
and 5 stacks with fewer than 5 coins..
Date due _______ Handed in: __
Homework H: Box-and-Whisker Plots
Determine the Five-Number Summary for each of the data sets of raisin counts, and construct
a box plot for each on the same scale. Then interpret the quantities in each Five-Number
Summary. In other words, use your results to answer the question “How many raisins are in a
half-ounce box of raisins?” for each brand.
Here are the raisin counts for boxes of Brand C raisins:
25 25 25 26 26 26 26 26 27 27 27 28 28 28 28 28 28 28 28 28 29 29 29 30 30 31 32 32
Here are the raisin counts for boxes of Brand D raisins:
23 24 25 25 25 27 27 27 27 27 27 27 27 28 28 29 29 29 29 29 29 30 31 32 32 33 33 33 34 34
35 35 35 36 36 38
Based on the interpretations you made in the above question, which brand of raisins would
you buy? Explain
Date due _______ Handed in: __
Homework I: Variation from the Mean
For the allocation below, find and interpret the MAD, variance, and standard deviation.
For the allocation below, find and interpret the MAD, variance, and standard deviation. (Note
that in this problem the mean is not a whole number, so there will be a fractional deviation for
each value. To simplify your work, round off each calculation to one decimal place.) What do
these calculations tell you about the data in this problem as compared to the data in the
previous problem?
Date due _______ Handed in: __
Homework J: How large are families?
Work through the problem-solving process to investigate the size of families in America. Type your
report.
Date due _______ Handed in: __
Homework K: Area under a curve
Find the area under the standard normal distribution:
between z = 1.56 and z = 2.22
between z = -0.62 and z = -1.33
between z = 1.48 and z = -1.75
to the right of z = 1.71
to the right of z = -0.96
to the left of z = -2.22
to the left of z = 1.96
Date due _______ Handed in: __
Homework L: Application questions
If the scores for a test are normally distributed and have a mean of 100 and a standard
deviation of 15, find the percentage of scores that will fall below 112.
Each month, an American household generates an average of 28 pounds of newspaper
for garbage or recycling. Assume the standard deviation is two pounds. If a household is
selected at random, find the probability of its generating between 27 and 31 pounds per
month. More than 30.2 pounds?
Assume that for a certain group of people, the mean for symbolic blood pressure is 120
and the standard deviation is 8 and the variable is normally distributed. Find the
percentage of individuals that who have a blood pressure between 120 and 130, above
126, and lower than 110.
The American Automobile Association reports that the average time it takes to respond
to an emergency call is 25 minutes. Assume the variable is approximately normally
distributed and the standard deviation is 4.5. If 80 calls are randomly selected,
approximately how many will be responded to in less than 15 minutes?
Date due _______ Handed in: __
Homework M: Comparison
SA student took two national standardized tests while applying for college. On the first
test the mean was 475 with standard deviation of 75. On the second test, the mean
was 32 with standard deviation of 6. If the student scored 630 on the first test and 45
on the second, on which test did he do better?
Date due _______ Handed in: __
Homework N: Linear Regression
See Worksheet
Date due _______ Handed in: __
Homework O: Non-Linear Regression
See Worksheet
Date due _______ Handed in: __
Homework P: Misuse of Statistics
From your reading on the misuse of statistics, please answer questions 1-21 odd.
Date due _______ Handed in: __
Other:
Project: Who’s the Greatest?
Stats Vocab
Bias
Mode
Population
Interval
Sample
Continuous data
Data
Histogram
Quantitative data
Stem and leaf plot
Qualitative data
Box plot
Random sample
Five-number summary
Variable
Quartiles
Variations
Interquartile range
Random error
Mean
Frequency
Allocation (fair& unfair)
Frequency table
Variance
Cumulative frequency
Standard deviation
Relative frequency
Bivariate data
Discrete data
Scatter plot
Distribution
Best fit line (regression equation)
Line plot
Normal distribution
Bar graph
Standard normal distribution
Median
z-scores
Algebra II - Statistics
Learning Targets
1. Four parts of the statistical problemsolving process
2. Identify variation in data and its
causes
3. Organize data in a stem plot
4. Organize data in a histogram
5. Determine mean, median and mode
6. Find a five number summary and
create a box plot
7. Compare data using box plots
8. Measure variation about the mean
9. Find the z-score for a specific data
value
10.Answer questions about normally
distributed data
11.Graph Bivariate data in a scatterplot
12.Find regression equations and use to
evaluate data.
5 Repeated demonstration of Mastery
4 You have totally mastered the skill
3 You have a firm grasp of the skill
2 You have some understanding of the skill
1 You have a weak understanding of the skill