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DESCRIPTIVE STATISTICS







STEM-AND-LEAF GRAPHS (STEMPLOTS), LINE GRAPHS, AND BAR GRAPHS

78 Practice Problems
View More
02:50
Understandable Statistics, Concepts and Methods 12th

The Boston Marathon is the oldest and best-known U.S. marathon. It covers a
route from Hopkinton, Massachusetts, to downtown Boston. The distance is
approximately 26 miles. The Boston Marathon web site has a wealth of information
about the history of the race. In particular, the site gives the winning times
for the Boston Marathon. They are all over 2 hours. The following data are the
minutes over 2 hours for the winning male runners over two periods of 20 years
each:
Earlier Period 2318 Recent
Period 9112315881816991913107169149172079151411102210871399910128923231819161715221310181516139201410912 Recent
Period 9891014711898118979910799
(a) Make a stem-and-leaf display for the minutes over 2 hours of the winning
times for the earlier period. Use two lines per stem.


Organizing Data
Stem-and-Leaf Displays

02:23
Understandable Statistics, Concepts and Methods 12th

Driving would be more pleasant if we didn't have to put up with the bad habits
of other drivers. USA Today reported the results of a Valvoline Oil Company
survey of 500 drivers, in which the drivers marked their complaints about other
drivers. The top complaints turned out to be tailgating, marked by 22%22% of the
respondents; not using turn signals, marked by 19%;19%; being cut off, marked by
16%;16%; other drivers driving too slowly, marked by 11%;11%; and other drivers
being inconsiderate, marked by 8%.8%. Make a Pareto chart showing percentage of
drivers listing each stated complaint. Could this information as reported be put
in a circle graph? Why or why not?


Organizing Data
Bar Graphs, Circle Graphs, and Time-Series Graphs

01:57
Understandable Statistics, Concepts and Methods 12th

How do college professors spend their time? The National Education Association
Almanac of Higher Education gives the following average distribution of
professional time allocation: teaching, 51%;51%; research, 16%;16%; professional
growth, 5%;5%; community service, 11%;11%; service to the college, 11%11%; and
consulting outside the college, 6%.6%. Make a pie chart showing the allocation
of professional time for college professors.


Organizing Data
Bar Graphs, Circle Graphs, and Time-Series Graphs



HISTOGRAMS, FREQUENCY POLYGONS, AND TIME SERIES GRAPHS

66 Practice Problems
View More
04:46
Statistics 1st

25 randomly selected students were asked the number of movies they watched the
previous week. The results are as follows:


 Number of Movies 01234 Frequency 59641 Relative Frequency  Cumulative Relative
Frequency  Number of Movies  Frequency  Relative Frequency  Cumulative Relative
Frequency 0519263441
a. Construct a histogram of the data.
b. Complete the columns of the chart.





Descriptive Statistics

03:03
Understandable Statistics, Concepts and Methods 12th

Decimal Data The following data represent tonnes of wheat harvested each year
(1894−1925)(1894−1925) from Plot 19 at the Rothamsted Agricultural Experiment
Stations, England.
2.711.622.601.642.202.021.671.992.341.261.312.711.622.601.642.202.021.671.992.341.261.31
1.802.822.152.071.621.472.190.591.480.772.041.802.822.152.071.621.472.190.591.480.772.04
1.320.891.350.950.941.391.191.180.460.701.320.891.350.950.941.391.191.180.460.70
(a) Multiply each data value by 100 to "clear" the decimals.
(b) Use the standard procedures of this section to make a frequency table and
histogram with your whole-number data. Use six classes.
(c) Divide class limits, class boundaries, and class midpoints by 100 to get
back to your original data values.


Organizing Data
Frequency Distributions, Histograms, and Related Topics

03:56
Understandable Statistics, Concepts and Methods 12th

The Wind Mountain excavation site in New Mexico is an important archaeological
location of the ancient Native American Anasazi culture. The following data
represent depths (in cm) below surface grade at which significant artifacts were
discovered at this site (Reference: A. I. Woosley and A. J. McIntyre, Mimbres
Mogollon Archaeology, University of New Mexico Press). Note: These data are also
available for download at the Companion Sites for this text.


85787595901510654512013770689068527580807073469982606512028753314590651540551004590140451257065751156570105956045305065756555955530508020085855812545707550658545756090901153055587812080656514065503012575137801201545706550459570702840125105758070906873755570956520075159046331006560558550106899145457545958565655282

Use seven classes.





Organizing Data
Frequency Distributions, Histograms, and Related Topics



MEASURES OF THE LOCATION OF THE DATA

9 Practice Problems
View More
10:52
Elementary Statistics a Step by Step Approach

The data shown represent the scores on a national achievement test for a group
of 10th-grade students. Find the approximate percentile ranks of these scores by
constructing a percentile
graph.
a. 220
b. 245
c. 276
d. 280
e. 300
 Score 196.5−217.5217.5−238.5238.5−259.5259.5−280.5280.5−301.5301.5−322.5 Frequency 5171748226 Score  Frequency 196.5−217.55217.5−238.517238.5−259.517259.5−280.548280.5−301.522301.5−322.56
For the same data, find the approximate scores that cor- respond to these
percentiles.
f. 15th
g. 29th
h. 43rd
i. 65th
j. 80th


Data Description
Measures of Position

09:21
Elementary Statistics a Step by Step Approach

The data show the population (in thousands) for a recent year of a sample of
cities in South Carolina.
2914232766262510202115379718111319121204317401293522586729261513175814253719406723109712129272018120356621114322
Find the data value that corresponds to each percentile.
a. 40th percentile
b. 75th percentile
c. 90th percentile
d. 30th percentile
Using the same data, find the percentile corresponding to the given data value.
e. 27
f. 40
g. 58
h. 67


Data Description
Measures of Position

03:11
Elementary Statistics a Step by Step Approach

To which percentile, quartile, and decile does the median correspond?


Data Description
Measures of Position



BOX PLOTS

11 Practice Problems
View More
04:23
Statistics Informed Decisions Using Data 4th

Explain how to determine the shape of a distribution using the boxplot and
quartiles.


Numerically Summarizing Data
The Five-Number Summary and Boxplots

04:38
Statistics Informed Decisions Using Data 4th

The following data represent the age of U.S. presidents on their respective
inauguration days (through Barack Obama).


42434646474748494950505151515152525454545454555555555656565757575758606161616264646568694247505254555761644348515254565761654649515455565761684649515455565862694750515455576064

(a) Find the five-number summary.
(b) Construct a boxplot.
(c) Comment on the shape of the distribution.




Numerically Summarizing Data
The Five-Number Summary and Boxplots

03:52
Statistics Informed Decisions Using Data 4th

After giving a statistics exam, Professor Dang determined the following
five-number summary for her class results: 60687789 98. Use this information to
draw a boxplot of the exam scores.


Numerically Summarizing Data
The Five-Number Summary and Boxplots



MEASURES OF THE CENTER OF THE DATA

36 Practice Problems
View More
02:01
Statistics Informed Decisions Using Data 4th

For each of the following situations, determine which measure of central
tendency is most appropriate and justify your reasoning.
(a) Average price of a home sold in Pittsburgh, Pennsylvania, in 2011
(b) Most popular major for students enrolled in a statistics course
(c) Average test score when the scores are distributed symmetrically
(d) Average test score when the scores are skewed right
(e) Average income of a player in the National Football League
(f) Most requested song at a radio station


Numerically Summarizing Data
Measures of Central Tendency

05:56
Statistics Informed Decisions Using Data 4th

Resistance and Sample Size Each of the following three data sets represents the
IQ scores of a random sample of adults. IQ scores are known to have a mean and
median of 100. For each data set, determine the mean and median. For each data
set recalculate the mean and median, assuming that the individual whose IQ is
106 is accidentally recorded as 160.160. For each sample size, state what
happens to the mean and the median. Comment on the role the number of
observations plays in resistance. (FIGURE CAN'T COPY)


Numerically Summarizing Data
Measures of Central Tendency

04:40
Statistics Informed Decisions Using Data 4th

Pulse Rates The following data represent the pulse rates (beats per minute) of
nine students enrolled in a section of Sullivan's Introductory Statistics
course. Treat the nine students as a population. (FIGURE CAN'T COPY)
(a) Determine the population mean pulse.
(b) Find three simple random samples of size 3 and determine the sample mean
pulse of each sample.
(c) Which samples result in a sample mean that overestimates the population
mean? Which samples result in a sample mean that underestimates the population
mean? Do any samples lead to a sample mean that equals the population mean?


Numerically Summarizing Data
Measures of Central Tendency



SKEWNESS AND THE MEAN, MEDIAN, AND MODE

48 Practice Problems
View More
01:45
Understandable Statistics, Concepts and Methods 12th

Interpretation A job-performance evaluation form has these categories:
1=1= excellent; 2=2= good; 3=3= satisfactory; 4=4= poor; 5=5= unacceptable
Based on 15 client reviews, one employee had
median rating of 4;4; mode rating of 1
The employee was pleased that most clients had rated her as excellent. The
supervisor said improvement was needed because at least half the clients had
rated the employee at the poor or unacceptable level. Comment on the different
perspectives.


Averages and Variation
Measures of Central Tendency: Mode, Median, and Mean

00:52
Statistics Informed Decisions Using Data 4th

Sketch four histograms-one skewed right, one skewed left, one bell-shaped, and
one uniform. Label each histogram according to its shape. What makes a histogram
skewed left? Skewed right? Symmetric?


Organizing and Summarizing Data
Organizing Quantitative Data: The Popular Displays

03:30
Elementary Statistics: Picturing the World 6th

Song Lengths Side-by-side box-and-whisker plots can be used to compare two or
more different data sets. Each box-and-whisker plot is drawn on the same number
line to compare the data sets more easily. The lengths (in seconds) of songs
played at two different concerts are shown.
(a) Describe the shape of each distribution. Which concert has less variation in
song lengths?
(b) Which distribution is more likely to have outliers? Explain your reasoning.
(c) Which concert do you think has a standard deviation of 16.3?16.3? Explain
your reasoning.
(d) Can you determine which concert lasted longer? Explain.


Descriptive Statistics
Measures of Position



MEASURES OF THE SPREAD OF THE DATA

19 Practice Problems
View More
07:26
Statistics Informed Decisions Using Data 4th

According to the U.S. Census Bureau, the mean of the commute time to work for a
resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard
deviation of the commute time is 8.1 minutes to answer the following:
(a) What minimum percentage of commuters in Boston has a commute time within 2
standard deviations of the mean?
(b) What minimum percentage of commuters in Boston has a commute time within 1.5
standard deviations of the mean? What are the commute times within 1.5 standard
deviations of the mean?
(c) What is the minimum percentage of commuters who have commute times between 3
minutes and 51.6 minutes?


Numerically Summarizing Data
Measures of Dispersion

01:25
Statistics Informed Decisions Using Data 4th

You have received a yearend bonus of $5000.$5000. You decide to invest the money
in the stock market and have narrowed your investment options down to two mutual
funds. The following data represent the historical quarterly rates of return of
each mutual fund for the past 20 quarters (5 years).
Describe each data set. That is, determine the shape, center, and spread. Which
mutual fund would you invest in and why?


Numerically Summarizing Data
Measures of Dispersion

01:46
Statistics Informed Decisions Using Data 4th

Suppose that you are in the market to purchase a car. With gas prices on the
rise, you have narrowed it down to two choices and will let gas mileage be the
deciding factor. You decide to conduct a little experiment in which you put 10
gallons of gas in the car and drive it on a closed track until it runs out gas.
You conduct this experiment 15 times on each car and record the number of miles
driven.
Describe each data set. That is, determine the shape, center, and spread. Which
car would you buy and why?


Numerically Summarizing Data
Measures of Dispersion



DESCRIPTIVE STATISTICS

20 Practice Problems
View More
02:36
Essentials of Statistics for Business and Economics 6th

Figure 1.8 provides a bar chart showing the amount of federal spending for the
years 2002 to 2008(USA Today, February 5,20082008(USA Today, February 5,2008 ).
a. What is the variable of interest?
b. Are the data categorical or quantitative?
c. Are the data time series or cross-sectional?
d. Comment on the trend in federal spending over time.


Data and Statistics

16:33
Mathematical Statistics with Applications 7th

Suppose that Y1,Y2,…,YnY1,Y2,…,Yn denote a random sample from the Poisson
distribution with mean λλ.
a. Find the MLE λˆλ^ for λλ
b. Find the expected value and variance of λ^λ^.
c. Show that the estimator of part (a) is consistent for λλ.
d. What is the MLE for P(Y=0)=e−λ?P(Y=0)=e−λ?


Properties of Point Estimators and Methods of Estimation
The Method of Maximum Likelihood

02:42
Mathematical Statistics with Applications 7th

In May 2005,2005, Tony Blair was elected to an historic third term as the
British prime minister. A Gallop U.K. poll
(http://gallup.com/poll/content/default.aspx?ci=1710, June 28, 2005) conducted
after Blair's election indicated that only 32%32% of British adults would like
to see their son or daughter grow up to become prime minister. If the same
proportion of Americans would prefer that their son or daughter grow up to be
president and 120 American adults are interviewed, a. what is the expected
number of Americans who would prefer their child grow up to be president?
b. what is the standard deviation of the number YY who would prefer that their
child grow up to be president?
c. is it likely that the number of Americans who prefer that their child grow up
to be president exceeds 40?


Discrete Random Variables and Their Probability Distributions
Tehebysheff’s Theorem



COEFFICIENT OF VARIATION

11 Practice Problems
View More
01:32
Elementary Statistics: Picturing the World 6th

Find the coefficient of variation for each of the two data sets. Then compare
the results.
The ages (in years) and weights (in pounds) of all wide receivers for the 2012
San Diego Chargers are listed.


 Yes 252424312528263022 Weights 215217190225192215185210220 Yes 252424312528263022 Weights 215217190225192215185210220




Descriptive Statistics
Measures of Variation

01:48
Elementary Statistics: Picturing the World 6th

Find the coefficient of variation for each of the two data sets. Then compare
the results.
Sample batting averages for baseball players from two opposing teams are listed.


 Team A 0.2950.2970.3100.3200.3250.3840.2720.2350.2560.297 Team
A 0.2950.3100.3250.2720.2560.2970.3200.3840.2350.297

 Team B 0.2230.2990.3120.2040.2560.2260.3000.2920.2380.260 Team
B 0.2230.3120.2560.3000.2380.2990.2040.2260.2920.260




Descriptive Statistics
Measures of Variation

01:44
Elementary Statistics: Picturing the World 6th

Find the coefficient of variation for each of the two data sets. Then compare
the results.
The ages (in years) and heights (in inches) of all pitchers for the 2013 St.
Louis Cardinals are listed.


 Ages  Heights 247229763773247326772576247232742275297523743179 Ages 242937242625243222292331 Heights 727673737776727475757479




Descriptive Statistics
Measures of Variation



QUARTILES, INTERQUARTILE RANGE, OUTLIERS AND Z-SCORE

44 Practice Problems
View More
01:09
Statistics Informed Decisions Using Data 4th

Explain what each quartile represents.


Numerically Summarizing Data
Measures of Position and Outliers

01:04
Statistics Informed Decisions Using Data 4th

Explain the circumstances for which the interquartile range is the preferred
measure of dispersion. What is an advantage that the standard deviation has over
the interquartile range?


Numerically Summarizing Data
Measures of Position and Outliers

02:35
Statistics Informed Decisions Using Data 4th

Explain the advantage of using zz -scores to compare observations from two
different data sets.


Numerically Summarizing Data
Measures of Position and Outliers



BOX-AND-WHISKER PLOT

17 Practice Problems
View More
02:50
Understandable Statistics, Concepts and Methods 12th

Some data sets include values so high or so low that they seem to stand apart
from the rest of the data. These data are called outliers. Outliers may
represent data collection errors, data entry errors, or simply valid but unusual
data values. It is important to identify outliers in the data set and examine
the outliers carefully to determine if they are in error. One way to detect
outliers is to use a box-and-whisker plot. Data values that fall beyond the
limits,


 Lower limit: Q1−1.5×(IQR) Upper limit: Q3+1.5×(IQR) Lower
limit: Q1−1.5×(IQR) Upper limit: Q3+1.5×(IQR)

where IQRIQR is the interquartile range, are suspected outliers. In the computer
software package Minitab, values beyond these limits are plotted with asterisks
(*). Students from a statistics class were asked to record their heights in
inches. The heights (as recorded) were
6569726768746450604557573677162526663806164746565726864605573715263617469677450475676266806465
(a) Make a box-and-whisker plot of the data.
(b) Find the value of the interquartile range (IQR)(IQR)
(c) Multiply the IQR by 1.5 and find the lower and upper limits.
(d) Are there any data values below the lower limit? above the upper limit? List
any suspected outliers. What might be some explanations for the outliers?




Averages and Variation
Percentiles and Box-and-Whisker Plots

01:14
Understandable Statistics, Concepts and Methods 12th

Angela took a general aptitude test and scored in the 82nd82nd percentile for
aptitude in accounting. What percentage of the scores were at or below her
score? What percentage were above?


Averages and Variation
Percentiles and Box-and-Whisker Plots

06:57
Elementary Statistics: Picturing the World 6th

Modified Boxplot AA modified boxplot is a boxplot that uses symbols to identify
outliers. The horizontal line of a modified boxplot extends as far as the
minimum data entry that is not an outlier and the maximum data entry that is not
an outlier. In Exercises 57 and 58,(a)58,(a) identify any outliers and (b) draw
a modified boxplot that represents the data set. Use asterisks (*) to identify
outtliers.


757880756272747580957672757880756272747580957672




Descriptive Statistics
Measures of Position



PERCENTAGE AND PERCENTILE

25 Practice Problems
View More
01:23
Statistics Informed Decisions Using Data 4th

Suppose you received the highest score on an exam. Your friend scored the
second-highest score, yet you both were in the 99th percentile. How can this be?


Numerically Summarizing Data
Measures of Position and Outliers

01:04
Statistics Informed Decisions Using Data 4th

Write a paragraph that explains the meaning of percentiles.


Numerically Summarizing Data
Measures of Position and Outliers

02:53
Statistics Informed Decisions Using Data 4th

The following graph is an ogive of the mathcmatics scorcs on the SAT for the
class of 2010. The vertical axis in an ogive is the cumulative relative
frequency and can also be interpreted as a percentile.
(a) Find and interpret the percentile rank of a student who scored 450 on the
SAT mathematics exam.
(b) Find and interpret the percentile rank of a student who scored 750 on the
SAT mathematics exam.
(c) If Jane scored at the 44 th percentile, what was her score?


Numerically Summarizing Data
Measures of Position and Outliers



HISTOGRAM

4 Practice Problems
View More
00:10
Elementary Statistics 13th

When using histograms to compare two data sets, it is sometimes difficult to
make comparisons by looking back and forth between the two histograms. A
back-to-back relative frequency histog ram has a format that makes the
comparison much easier. Instead of frequencies, we should use relative
frequencies (percentages or proportions) so that the comparisons are not
difficult when there are different sample sizes. Use the relative frequency
distributions of the ages of Oscarwinning actresses and actors from Exercise 19
in Section 2 - 1 on page 49,49, and complete the back-to-back relative frequency
histograms shown below. Then use the result to compare the two data sets.
(GRAPH CAN'T COPY)


Exploring Data with Tables and Graphs
Histograms

00:14
Elementary Statistics 13th

Answer the questions by referring to the following Minitab-generated histogram,
which depicts the weights (grams) of all quarters listed in Data Set 29 "Coin
Weights" in Appendix BB. (Grams are actually units of mass and the values shown
on the horizontal scale are rounded.)
How would the shape of the histogram change if the vertical scale uses relative
frequencies expressed in percentages instead of the actual frequency counts as
shown here?
(GRAPH CAN'T COPY)


Exploring Data with Tables and Graphs
Histograms

00:35
Elementary Statistics 13th

If we collect a sample of blood platelet counts much larger than the sample
included with Exercise 3,3, and if our sample includes a single outlier, how
will that outlier appear in a histogram?



Exploring Data with Tables and Graphs
Histograms



ROOT MEAN SQUARE

1 Practice Problems
View More
00:48
Statistics

The r.m.s. error of the regression line for predicting yy from xx is
 (i)  (ii)  (iii) r×SD of y SD of y SD of x (vi) 1−r2−−−−−√× SD of x (iv) r× SD
of x (v) 1−r2−−−−−√× SD of y (i)  SD of y (iv) r× SD of x (ii)  SD
of x (v) 1−r2× SD of y (iii) r×SD⁡ of y (vi) 1−r2× SD of x


The R.M.S. Error for Regression



ERRORS AND OUTLIERS

5 Practice Problems
View More
01:49
STATS Modeling The World (statistics)

Elephants and hippos We removed humans from the scatterplot in Exercise 31
because our species was an outlier in life expectancy. The resulting scatterplot
shows two points that now may be of concern. The point in the upper right corner
of this scatterplot is for elephants, and the other point at the far right is
for hippos.
a) By removing one of these points, we could make the association appear to be
stronger. Which point? Explain.
b) Would the slope of the line increase or decrease?
c) Should we just keep removing animals to increase the strength of the model?
Explain.
d) If we remove elephants from the scatterplot, the slope of the regression line
becomes 11.6 days per year. Do you think elephants were an influential point?
Explain.


Exploring Relationships Between Variables
Regression Wisdom

01:47
STATS Modeling The World (statistics)

Swim the lake 2010 People swam across Lake Ontario 48 times between 1974 and
2010 (www.soloswims.com). We might be interested in whether they are getting any
faster or slower. Here are the regression of the crossing Times (minutes)
against the Year of the crossing and the residuals plot:
a) What does the R2R2 mean for this regression?
b) Are the swimmers getting faster or slower? Explain.
c) The outlier seen in the residuals plot is a crossing by Vicki Keith in 1987
in which she swam a round trip, north to south, and then back again. Clearly,
this swim doesn't belong with the others. Would removing it change the model a
lot? Explain.


Exploring Relationships Between Variables
Regression Wisdom

03:35
STATS Modeling The World (statistics)

Tracking hurricanes 2010 In a previous chapter, we saw data on the errors (in
nautical miles) made by the National Hurricane Center in predicting the path of
hurricanes. The scatterplot below shows the trend in the 24-hour tracking errors
since 1970 (www.nhc.noaa.gov).
a) Interpret the slope and intercept of the model.
b) Interpret se in this context.
c) The Center would like to achieve an average tracking error of 45 nautical
miles by 2015. Will they make it? Defend your response.
d) What if their goal were an average tracking error of 25 nautical miles?
e) What cautions would you state about your conclusion?


Exploring Relationships Between Variables
Regression Wisdom



CHEBYSHEV’S INEQUALITY

2 Practice Problems
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04:17
Statistics Informed Decisions Using Data 4th

A popular theory in investment states that you should invest a certain amount of
money in foreign investments to reduce your risk. The risk of a portfolio is
defined as the standard deviation of the rate of return. Refer to the graph on
the following page, which depicts the relation between risk (standard deviation
of rate of return) and reward (mean rate of return).
(a) Determine the average annual return and level of risk in a portfolio that is
10%10% foreign.
(b) Determine the percentage that should be invested in foreign stocks to best
minimize risk.
(c) Why do you think risk initially decreases as the percent of foreign
investments increases?
(d) A portfolio that is 30%30% foreign and 70%70% American has a mean rate of
return of about 15.8%,15.8%, with a standard deviation of 14.3%.14.3%. According
to Chebyshev's Inequality, at least 75%75% of returns will be between what
values? According to Chebyshev's Inequality, at least 88.9%88.9% of returns will
be between what two values? Should an investor be surprised if she has a
negative rate of return? Why?


Numerically Summarizing Data
Measures of Dispersion

0:00
Statistics Informed Decisions Using Data 4th

Chebyshev's Inequality applies to all distributions regardless of shape, but the
Empirical Rule holds only for distributions that are bell shaped.


Numerically Summarizing Data
Measures of Dispersion



VARIANCE, STANDARD DEVIATION, AND RANGE

11 Practice Problems
View More
01:35
Statistics Informed Decisions Using Data 4th

Which of the following would have a higher standard deviation? (a) IQ of
students on your campus or (b) IQ of residents in your home town? Why?


Numerically Summarizing Data
Measures of Dispersion

02:38
Statistics Informed Decisions Using Data 4th

Are any of the measures of dispersion mentioned in this section resistant?
Explain.


Numerically Summarizing Data
Measures of Dispersion

01:53
Statistics Informed Decisions Using Data 4th

Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You
need to decide which professor to take the class from and have just completed
your Introductory Statistics course. Records obtained from past students
indicate that students in Professor Alpha's class have a mean score of 80%80%
with a standard deviation of 5%,5%, while past students in Professor Omega's
class have a mean score of 80%80% with a standard deviation of 10%.10%. Decide
which instructor to take for Introductory Biology using a statistical argument.


Numerically Summarizing Data
Measures of Dispersion



MEASURES OF DISPERSION

19 Practice Problems
View More
03:36
Statistics Informed Decisions Using Data 4th

Use the following steps to approximate the median from grouped data.
Step 1 Construct a cumulative frequency distribution.
Step 2 Identify the class in which the median lies. Remember, the median can be
obtained by determining the observation that lies in the middle.
Step 3 Interpolate the median using the formula


 Median =M=L+n2−CFf(i) Median =M=L+n2−CFf(i)

where LL is the lower class limit of the class containing the median nn is the
number of data values in the frequency distribution CF is the cumulative
frequency of the class immediately preceding the class containing the median ff
is the frequency of the median class ii is the class width of the class
containing the median.
Approximate the median of the frequency distribution in Problem 4.




Numerically Summarizing Data
Measures of Central Tendency and Dispersion rouped Data

04:56
Statistics Informed Decisions Using Data 4th

The data on the next page represent the age of the mother at childbirth for 1980
and 2007 . (TABLE CAN'T COPY)
(a) Approximate the population mean and standard deviation of age for mothers in
1980 .
(b) Approximate the population mean and standard deviation of age for mothers in
2007
(c) Which year has the higher mean age?
(d) Which year has more dispersion in age?


Numerically Summarizing Data
Measures of Central Tendency and Dispersion rouped Data

06:57
Statistics Informed Decisions Using Data 4th

The following data represent the male and female population, by age, of the
United States in 2008 Note: Use 95 for the class midpoint of ≥90.≥90.


 Age 0−910−1920−2930−3940−4950−5960−6970−7980−89≥90 Source: U.S. Census
Bureau  Male Resident Pop  (in
thousands) 92921,07421,10519,78021,75419,30312,38869403106479 Female
Resident  Pop (in
thousands) 19,99220,27820,48220,04222,34620,30213,709883791541263 Age  Male
Resident Pop  (in thousands)  Female Resident  Pop (in
thousands) 0−992919,99210−1921,07420,27820−2921,10520,48230−3919,78020,04240−4921,75422,34650−5919,30320,30260−6912,38813,70970−796940883780−8931069154≥904791263 Source:
U.S. Census Bureau 

(a) Approximate the population mean and standard deviation of age for males.
(b) Approximate the population mean and standard deviation of age for females.
(c) Which gender has the higher mean age?
(d) Which gender has more dispersion in age?




Numerically Summarizing Data
Measures of Central Tendency and Dispersion rouped Data



FIVE-NUMBER SUMMARY

3 Practice Problems
View More
01:02
Statistics Informed Decisions Using Data 4th

What does the five-number summary consist of?


Numerically Summarizing Data
The Five-Number Summary and Boxplots


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