Download Unit 4: Statistics

Name__________________________
Unit 4: Statistics
Show all work!
Date____________
Worksheet A4 (Part I)
(Measures of Central Tendency
Adapted from IV-16 Finite Bounded Book)
Show work
1. Calculate the mean, median and mode for each of the following:
a.) 2, 8, 7, 8, 5, 8, 10, 5
b.) 18, 22, 22, 17, 30, 18, 12
c.) 5, 5, 5, 5, 10
2. If each of six students scored 80 on a test, find each of the following for
the set of 6 scores:
a.) Mean
Median
Mode
b.) Make up a set of 6 scores that are not all the same but that have a
mean, median and mode of 80.
3. The mean score on a set of 20 tests is 75. What is the sum of the score?
4. The tram at a ski area has a capacity of 50 people with a load weight limit of
7500 lbs. What is the mean weight of the passengers if the tram is loaded to
capacity?
5. The names and ages for each person in a family of five follow:
Name
Age
Don
40
Jane
36
Kirk
8
Jean
6
Scott
2
a.) What is the mean age?
b.) Find the mean in 5 years from now (everyone is 5 years older).
Hint: Make a new chart which shows each person’s age 5 years from now.
c.) Find the mean in 10 years from now.
d.) Describe the relationship among the answers you found in parts a-c. Do
you see a pattern? Describe it.
6. Suppose you own a hat shop and decide to order hats in only one size for
the coming season. To decide which size to order, you look at last year’s
sales figures, which are itemized according to size. Should you find the
mean, median or mode for the data? Explain your answer with words (be
clear).
Name__________________________
Unit 4: Statistics
Date____________
Worksheet A4 (Part II)
(Adapted from IV-17 Finite Bounded Book)
Show work (if you use a calculator, show me what you put into the calculator).
1. The following table gives the annual salaries of the 40 dancers of a certain
troupe.
a.)
Find the mean annual salary for the troupe
Hint: 2 dancers made $18,000 so multiply 2 times 18,000, do this for all
the dancers
Salary
Number of
Salary x # of
Dancers
Dancers
$18,000
2
$36,000
$22,000
4
$26,000
4
b.) Find the median salary.
$35,000
3
Hint: Is there ONE middle
$38,000
12
number or TWO?
$44,000
8
$50,000
4
$80,000
2
$150,000
1
c.)
Find the mode.
2. If Janet traveled 45 miles in 90 minutes, what was her mean speed?
3. The youngest person at Google is 17 and the range of ages at Google is 27
years. How old is the oldest person at Google?
4. Choose the set of numbers that fits the descriptions given in each of the
following:
a. Choose the set that has a mean of 6 and a range of 6
Set A:
3, 5, 7, 9
Set B:
2, 4, 6, 8
Set C:
2, 3, 4, 15
b. Choose the set that has a mean of 11, a median of 11, and a mode of 11
Set A:
9, 10, 10, 11, 12, 12, 13
Set B:
10, 11, 11, 11, 11, 11, 14
Set C:
9, 11, 11, 11, 11, 12, 12
c. Choose the set that has a mean of 3, a median of 3 and has no mode
Set A:
0, 2.5, 6.5
Set B:
1, 3, 3, 5
Set C:
1, 2, 4, 5
Name__________________________
Unit 4: Statistics
Date____________
Worksheet B4
(Measures of VariationAdapted from IV-17 Finite Bounded Book)
Show work (if you use a calculator, show me what you put into the calculator).
1. What is the standard deviation of the heights of seven trapeze artists if
there heights are 175 cm, 182 cm, 190 cm, 180 cm, 192 cm, 172 cm and 190 cm?
Use the table below to guide
xi (heights) xi  x
( xi  x ) 2
For the middle column, find the mean and subtract the mean from each height.
For the last column, square the middle column. Now add the last column and
divide by n. Do you remember the last step?
2. If all the numbers in a set are equal, what is the standard deviation? For
instance, suppose you are in Hawaii and it’s 80 degrees every day, what is
the standard deviation?
3. Go on-line or watch the weather and find out the daytime high temperature
for the next 4 days (starting tomorrow). List those here: ___ ____ ____ ____
a.) Find the mean_____________
c.) Find the mode____________
b.) Find the median_____________ d.) Find the standard deviation (create a table
like the one – use the back or a separate sheet)
Review on Measures of Center
4. To receive an A in a class, Will needs at least a mean of 90 on 5 exams. Will’s
grades on the first 4 exams were 84, 95, 86 and 94. What is the minimum
score he needs on the fifth exam to earn an A in the class (he needs a 90 or
more – no rounding up).
5. The mean of 5 numbers is 6. If one of the 5 numbers is removed, the mean
becomes 7. What is the value of the number that was removed? Try some
values if you can’t figure it out.
Challenge (this is very doable)
6. Ginny’s median score on 3 tests was 90. Her mean score was 92 and her
range was 6. What were her 3 test scores?
Name__________________________
Unit 4: Statistics
Date____________
Worksheet C4 (Part I)
Frequency Tables
Needs to be scanned
Will be given to you in class
Name__________________________
Unit 4: Statistics
Date____________
Worksheet C4 (Part II)
(Measures of Variation
Adapted from IV-17 Finite Bounded Book)
Show work: graphs/charts need to be neat )use a ruler or straightedge
Make a frequency table and histogram for each data set.
#1. The following are the ounces in canned goods of 18 cans: 11, 15, 16, 16, 14, 15, 10, 8, 8, 12, 15,
16, 8, 15, 8, 14, 10, 10
Histogram Here (neatly)
Size (ounces)
Frequency
2.) Make a grouped frequency table for the following Berwyn June temperatures:
75, 78, 99, 88, 74, 89, 61, 91, 84, 78, 75, 92, 88, 67, 82, 85
Finish Table
Class
Frequency
60-69
70-79
Name__________________________
Unit 4: Statistics
Date____________
Worksheet D4 (Part I)
Stem and Leaf Plots, Histograms, and Circle Graphs
Needs to be scanned
Will be given to you in class
Name__________________________
Unit 4: Statistics
Date____________
Worksheet D4 (Part II)
3.) Make a circle graph for the following
Students were asked about their favorite type of music. The responses of 500 students are recorded
in the following table.
HINT: Divide the number of students choosing each genre by the total number of students
surveyed. Then multiply by the TOTAL number of degrees in the circle.
(Round degree measures to the nearest degree).
USE a PROTRACTOR to measure degree. I gave you a radius as a starting point.
Classical
Rock
R&B
Country
Hip-Hop
Emo
43
115
181
57
78
26
Name__________________________
Unit 4: Statistics
Date____________
Worksheet E4
(Adapted from IV-17 Finite Bounded Book)
1. Construct a boxplot for the following mileages per gallon of various company cars:
22
18
14
28
30
12
38
22
30
39
20
18
14
16
10
Be sure to draw a number line with an appropriate scale. Be neat.
Min:______
Q1:______
Q2(Med):______
Range:________
Q3:______
Max:______
IQR:________
2. Following are boxplots comparing ticket prices of two performing arts theaters:
a. What is the median ticket price for each theater?
b. Which theater has the greatest range of prices?
c. What is the highest ticket price at either theater?
d. Draw 2 conclusions comparing the ticket prices at Theater A versus Theater B
(Be specific.)
Box Office Ticket Prices
Theatre A
Theatre B
0
10
20
Conclusion 1:
Conclusion 2:
30
40
50
60
70
80
90
100
3. Construct a boxplot (neatly please) for the following set of test scores. Indicate
outliers, if any, with asterisks.
Using the 1.5  IQR, show if there are outliers. Remember to add this value to Q3
and subtract
it from Q1 to help determine if you have an outlier.
Data: 20
95
40
70
90 70
80
80
90
95
4. Using the following 8 daytime temperatures from Hawaii's Big Island: 80, 84, 80, 81, 84,
82, 82, 84, add a 9th temperature so there is no right whisker.
What is your added temperature:___________
What 2 values must be equal so there is no right whisker:___________________
Use your 9 temperatures and draw a boxplot below (always be neat, draw a number line
and show your scale).
Extra Credit:
Find the next 10-day temps for Tampa Bay, Florida. Using your same number line above,
create a boxplot below the one you just created using your Tampa Bay temperatures.
Draw 2 conclusions based on your side-by-side boxplots of Tampa Bay, Florida and
Hawaii's Big Island.
Name__________________________
Unit 4: Statistics
Show all work!
Date____________
Worksheet F4
Needs to be scanned
Will be given to you in class
Name__________________________
Unit 4: Statistics
Date____________
Worksheet G4
For every question: Fill in z-scores, mean, and mean +/-standard deviations for
each z-score on the sketch.
1. The mean IQ score for 1500 students is 100, with a standard deviation of
15. Assuming the scores have a normal curve, determine the following.
a.) How many have an IQ between 85
and 115? (Hint: Find the percent first
and then multiply by 1500.)
b.) How many have an IQ between 70
and 130? (Hint: Find the percent first
and then multiply by 1500.)
c.) How many have an IQ over 145? (Hint: Find the percent that has under a 145 and
then subtract.)
2. Sugar Plops boxes claim to hold 16oz. To make sure they do, the
manufacturer fills the box to a mean weight of 16.1 oz, with a standard
deviation of 0.05 oz.
a.) If the weights have a normal curve, what
percent of the boxes actually contain 16 oz.
or MORE?
3. For certain workers, the mean wage is $5.00/hr, with a standard deviation of
$0.50.
Assuming a normal distribution, what is the
probability that the worker’s wage is between
$4.50 and $5.50?
4. A job applicant test consisted of three parts: verbal, quantitative, and
logical reasoning. The mean and standard deviation for each part are as
follows:
Mean (x-bar)
Stand. Dev (s)
Verbal
Quantitative
Logical
Reasoning
84
10
118
18
14
4
a.) Holly’s scores were 90 on verbal, 113 on
quantitative and 18 on logical reasoning.
Determine her z-score for each part.
(show setup)Verbal z-score:__________
score:_________
Quant. z-score:__________ Logical z-
b.) Use the answers in part a to answer the following:
(i)
On which part did she perform relatively the highest?_________________
(ii)
On which part did she perform relatively the lowest?_________________
5. The average phone call in a certain town lasts 4 min with a standard
deviation of 2 minutes. Assume a normal distribution.
a.) What percent of calls lasts fewer than 2
minutes?
b.) What percent of calls lasts greater than
6 minutes?
6. According to psychologists, IQs are normally distributed with a mean of 100
and a standard deviation of 15.
a.) What percent of the population have
IQs between 100 and 130? (Use your
normal curve with percents).
b.) What percent of the population have
IQs lower than 85?
c.) What percent of the population have
IQs greater than 85?
Name__________________________
Unit 4: Statistics
Date____________
Worksheet H4
Unit 4 Finite Math Jeopardy Problems
Measures
of Central
Tendency
Frequency 5 Summary Variance &
Normal
Tables & Values and Standard Distribution
Histograms Box Plots Deviation
100:
What is the mode
of the following
data?
5, 7, 8, 5, 6, 6
100:
Make a frequency
table to organize
the following data.
6, 5, 6, 6, 4, 4, 6
100:
Find the range of
the following data.
57, 80, 63, 42, 38,
43, 34, 35, 58
100:
Calculate the
variance for the
following set of
data.
5, 7, 8, 5, 6, 6
100:
If the mean age of
students in a class
is 16, and Molly is
16, what is her zscore?
200:
What is the median
of the following
data?
12, 18, 13, 11, 17
200:
Make a grouped
frequency table to
organize the
following data, and
use it to
ESTIMATE the
mean.
6, 15, 32, 12, 18, 8,
3, 4, 9
200:
Find the Quartiles
and inner quartile
range of the
following data.
57, 80, 63, 42, 38,
43, 34, 35, 58
200:
Calculate the
standard deviation
for the following
set of data.
5, 7, 8, 5, 6, 6
300:
What is the mean of
the following data?
24, 36, 12, 18, 26,
32, 33
300:
Make a histogram
using the grouped
frequency table
from 200.
(6, 15, 32, 12, 18, 8,
3, 4, 9)
300:
Make a box plot to
represent the
following data.
57, 80, 63, 42, 38,
43, 34, 35, 58
300:
Calculate the
variance and
standard deviation
for the following
set of data.
12, 18, 13, 11, 17
200:
2500 students took
the SAT’s on a
given day in
Chester County.
The mean was a
1130 and the
standard deviation
was 130. How
many students
scored between an
870 and a 1390?
300:
The mean IQ score
in the US is a 100
with a standard
deviation of 15. If
Joe scores a 93,
what percentage of
people score lower
than him?