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Construct a frequency polygon of U.S. Presidents’ ages at inauguration shown in [link] .

Age at Inauguration Frequency
41.5–46.5 4
46.5–51.5 11
51.5–56.5 14
56.5–61.5 9
61.5–66.5 4
66.5–71.5 2

The first label on the x -axis is 39. This represents an interval extending from 36.5 to 41.5. Since there are no ages less than 41.5, this interval is used only to allow the graph to touch the x -axis. The point labeled 44 represents the next interval, or the first “real” interval from the table, and contains four scores. This reasoning is followed for each of the remaining intervals with the point 74 representing the interval from 71.5 to 76.5. Again, this interval contains no data and is only used so that the graph will touch the x -axis. Looking at the graph, we say that this distribution is skewed because one side of the graph does not mirror the other side.

This figure shows a graph entitled, 'President's Age at Inauguration.' The x-axis is labeled 'Ages' and is marked off at 39, 44, 49, 54, 59, 64, 69 and 74. The y-axis is labeled, 'Frequency,' and is marked off in intervals of 1 from 0 to 15. The following points are plotted and a line connects one to the other to create the frequency polygon: (39, 0), (44, 4), (49, 11), (54, 14), (59, 9), (64, 4), (69, 2), (74, 0).
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Frequency polygons are useful for comparing distributions. This is achieved by overlaying the frequency polygons drawn for different data sets.

We will construct an overlay frequency polygon comparing the scores from [link] with the students’ final numeric grade.

Frequency Distribution for Calculus Final Test Scores
Lower Bound Upper Bound Frequency Cumulative Frequency
49.5 59.5 5 5
59.5 69.5 10 15
69.5 79.5 30 45
79.5 89.5 40 85
89.5 99.5 15 100
Frequency Distribution for Calculus Final Grades
Lower Bound Upper Bound Frequency Cumulative Frequency
49.5 59.5 10 10
59.5 69.5 10 20
69.5 79.5 30 50
79.5 89.5 45 95
89.5 99.5 5 100
This is an overlay frequency polygon that matches the supplied data. The x-axis shows the grades, and the y-axis shows the frequency.
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Suppose that we want to study the temperature range of a region for an entire month. Every day at noon we note the temperature and write this down in a log. A variety of statistical studies could be done with this data. We could find the mean or the median temperature for the month. We could construct a histogram displaying the number of days that temperatures reach a certain range of values. However, all of these methods ignore a portion of the data that we have collected.

One feature of the data that we may want to consider is that of time. Since each date is paired with the temperature reading for the day, we don‘t have to think of the data as being random. We can instead use the times given to impose a chronological order on the data. A graph that recognizes this ordering and displays the changing temperature as the month progresses is called a time series graph.

Constructing a time series graph

To construct a time series graph, we must look at both pieces of our paired data set . We start with a standard Cartesian coordinate system. The horizontal axis is used to plot the date or time increments, and the vertical axis is used to plot the values of the variable that we are measuring. By doing this, we make each point on the graph correspond to a date and a measured quantity. The points on the graph are typically connected by straight lines in the order in which they occur.

The following data shows the Annual Consumer Price Index, each month, for ten years. Construct a time series graph for the Annual Consumer Price Index data only.

Year Jan Feb Mar Apr May Jun Jul
2003 181.7 183.1 184.2 183.8 183.5 183.7 183.9
2004 185.2 186.2 187.4 188.0 189.1 189.7 189.4
2005 190.7 191.8 193.3 194.6 194.4 194.5 195.4
2006 198.3 198.7 199.8 201.5 202.5 202.9 203.5
2007 202.416 203.499 205.352 206.686 207.949 208.352 208.299
2008 211.080 211.693 213.528 214.823 216.632 218.815 219.964
2009 211.143 212.193 212.709 213.240 213.856 215.693 215.351
2010 216.687 216.741 217.631 218.009 218.178 217.965 218.011
2011 220.223 221.309 223.467 224.906 225.964 225.722 225.922
2012 226.665 227.663 229.392 230.085 229.815 229.478 229.104
Year Aug Sep Oct Nov Dec Annual
2003 184.6 185.2 185.0 184.5 184.3 184.0
2004 189.5 189.9 190.9 191.0 190.3 188.9
2005 196.4 198.8 199.2 197.6 196.8 195.3
2006 203.9 202.9 201.8 201.5 201.8 201.6
2007 207.917 208.490 208.936 210.177 210.036 207.342
2008 219.086 218.783 216.573 212.425 210.228 215.303
2009 215.834 215.969 216.177 216.330 215.949 214.537
2010 218.312 218.439 218.711 218.803 219.179 218.056
2011 226.545 226.889 226.421 226.230 225.672 224.939
2012 230.379 231.407 231.317 230.221 229.601 229.594
This is a times series graph that matches the supplied data. The x-axis shows years from 2003 to 2012, and the y-axis shows the annual CPI.
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Questions & Answers

what is standard deviation?
Jawed Reply
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Yeah....the simplest one
what is the number of x
Godgift Reply
Javed Arif
how will you know if a group of data set is a sample or population
Kingsley Reply
population is the whole set and the sample is the subset of population.
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Pls I hv a problem on t test is there anyone who can help?
What's your problem Peggy Abang
Bhavika is right
what is the problem peggy?
hii Bhavika
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
three coins are tossed. find the probability of no head
Kanwal Reply
three coins are tossed consecutively or what ?
p(getting no head)=1/8
or .125 is the probability of getting no head when 3 coins are tossed
what is two tailed test
Umar Reply
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
in this test you are worried on both the ends
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
In order to apply weddles rule for numerical integration what is minimum number of ordinates
Anjali Reply
excuse me?
didn't understand the question though.
which question? ?
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
geometric mean of two numbers 4 and 16 is:
iphone Reply
quartile deviation of 8 8 8 is:
sorry 8 is the geometric mean of 4,16
quartile deviation of 8 8 8 is
can you please expalin the whole question ?
can you please post the picture of that ?
10 now
how to find out the value
srijth Reply
can you be more specific ?
what is the difference between inferential and descriptive statistics
Eze Reply
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
if you need more help i am up for the help.
Thanks a lot
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
my pleasure😊. Helping others offers me satisfaction 😊
for poisson distribution mean............variance.
mehul Reply
both are equal to mu
what is a variable
Bonolo Reply
something that changes
why we only calculate 4 moment of mean? asked in papers.
Faizan Reply
why we only 4 moment of mean ? asked in BA exam
Good evening, can you please help me by sharing regression and correlation analysis notes....thank you in advance
Refiloe Reply
Hello, can you please share the possible questions that are likely to be examined under the topic: regression and correlation analysis.
for normal distribution mean is 2 & variance is 4 find mu 4?
Faizan Reply
repeat quastion again
find mu 4. it can be wrong but want to prove how.
for a normal distribution if mu 4 is 12 then find mu 3?
Faizan Reply
Question hi wrong ha
ye BA mcqs me aya he teen he. 2dafa aya he
if X is normally distributed. (n,b). then its mean deviation is?
The answer is zero, because all odd ordered central moments of a normal distribution are Zero.
which question is zero
sorry it is (5,16) in place of (n,b)
I got. thanks. it is zero.
a random variable having binomial distribution is?

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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