2.1 Stem-and-leaf graphs (stemplots), line graphs, and bar graphs  (Page 3/5)

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Try it

The population in Park City is made up of children, working-age adults, and retirees. [link] shows the three age groups, the number of people in the town from each age group, and the proportion (%) of people in each age group. Construct a bar graph showing the proportions.

Age groups Number of people Proportion of population
Children 67,059 19%
Retirees 131,662 38%

The columns in [link] contain: the race or ethnicity of students in U.S. Public Schools for the class of 2011, percentages for the Advanced Placement examine population for that class, and percentages for the overall student population. Create a bar graph with the student race or ethnicity (qualitative data) on the x -axis, and the Advanced Placement examinee population percentages on the y -axis.

Race/Ethnicity AP Examinee Population Overall Student Population
1 = Asian, Asian American or Pacific Islander 10.3% 5.7%
2 = Black or African American 9.0% 14.7%
3 = Hispanic or Latino 17.0% 17.6%
4 = American Indian or Alaska Native 0.6% 1.1%
5 = White 57.1% 59.2%
6 = Not reported/other 6.0% 1.7%

Try it

Park city is broken down into six voting districts. The table shows the percent of the total registered voter population that lives in each district as well as the percent total of the entire population that lives in each district. Construct a bar graph that shows the registered voter population by district.

District Registered voter population Overall city population
1 15.5% 19.4%
2 12.2% 15.6%
3 9.8% 9.0%
4 17.4% 18.5%
5 22.8% 20.7%
6 22.3% 16.8%

References

Burbary, Ken. Facebook Demographics Revisited – 2001 Statistics, 2011. Available online at http://www.kenburbary.com/2011/03/facebook-demographics-revisited-2011-statistics-2/ (accessed August 21, 2013).

“9th Annual AP Report to the Nation.” CollegeBoard, 2013. Available online at http://apreport.collegeboard.org/goals-and-findings/promoting-equity (accessed September 13, 2013).

“Overweight and Obesity: Adult Obesity Facts.” Centers for Disease Control and Prevention. Available online at http://www.cdc.gov/obesity/data/adult.html (accessed September 13, 2013).

Chapter review

A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends. That is, finding a general pattern in data sets including temperature, sales, employment, company profit or cost over a period of time. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulative effect (stacked bar graphs). Bar graphs are especially useful when categorical data is being used.

For each of the following data sets, create a stem plot and identify any outliers.

The miles per gallon rating for 30 cars are shown below (lowest to highest).
19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 38, 38, 38, 41, 43, 43

Stem Leaf
1 9 9 9
2 0 1 1 5 5 5 6 6 8 9
3 1 1 2 2 3 4 5 6 7 7 8 8 8 8
4 1 3 3

The height in feet of 25 trees is shown below (lowest to highest).
25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

The data are the prices of different laptops at an electronics store. Round each value to the nearest ten.
249, 249, 260, 265, 265, 280, 299, 299, 309, 319, 325, 326, 350, 350, 350, 365, 369, 389, 409, 459, 489, 559, 569, 570, 610

Stem Leaf
2 5 5 6 7 7 8
3 0 0 1 2 3 3 5 5 5 7 7 9
4 1 6 9
5 6 7 7
6 1

The data are daily high temperatures in a town for one month.
61, 61, 62, 64, 66, 67, 67, 67, 68, 69, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 95

For the next three exercises, use the data to construct a line graph.

In a survey, 40 people were asked how many times they visited a store before making a major purchase. The results are shown in [link] .

Number of times in store Frequency
1 4
2 10
3 16
4 6
5 4

In a survey, several people were asked how many years it has been since they purchased a mattress. The results are shown in [link] .

Years since last purchase Frequency
0 2
1 8
2 13
3 22
4 16
5 9

Several children were asked how many TV shows they watch each day. The results of the survey are shown in [link] .

Number of TV Shows Frequency
0 12
1 18
2 36
3 7
4 2

The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. [link] shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students.

Seasons Number of students Proportion of population
Spring 8 24%
Summer 9 26%
Autumn 11 32%
Winter 6 18%

Using the data from Mrs. Ramirez’s math class supplied in [link] , construct a bar graph showing the percentages.

David County has six high schools. Each school sent students to participate in a county-wide science competition. [link] shows the percentage breakdown of competitors from each school, and the percentage of the entire student population of the county that goes to each school. Construct a bar graph that shows the population percentage of competitors from each school.

High School Science competition population Overall student population
Alabaster 28.9% 8.6%
Concordia 7.6% 23.2%
Genoa 12.1% 15.0%
Mocksville 18.5% 14.3%
Tynneson 24.2% 10.1%
West End 8.7% 28.8%

Use the data from the David County science competition supplied in [link] . Construct a bar graph that shows the county-wide population percentage of students at each school.

how to use grouped and ungrouped data
Just a test from gplay
how come 5.67
by dividing 11.37 on 2
saifuddin
by dividing 11.34 on 2
saifuddin
what is index number?
vinayak
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fit a binomial distribution for the following data and test the goodness of fit x: 0 1 2 3 4 5 6 f: 5 18 28 12 7 6 4
solution
Mano
Mano
Simonsakala
It is a square chi
Nelson
But can't be a binomial because, the x numbers are 0 to 6, instead those would be "0" or "1" in a straight way
Nelson
You can do a chi-square test, but the assumption has to be a normal distribution, and the last f's number need to be "64"
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sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
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rajendra
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Sorry I see my mistake, we have to calculate the expected values
Nelson
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
Nelson
why it is not possible brother
ibrar
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
Nelson
so after we calculate the expected values for each observed value (f) we do the chi-square. x^2=summatory(observed-expected)^2 / expected and compare with x^2 in table with 0.8
Nelson
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
Nelson
It is possible, sorry for my mistake
Nelson
two trader shared investment and buoght Cattle.Mr.Omer bought 255 cows & rented the farm for a period of 32 days. Mr. Ahmed grazed his Cattle for 25 days. Mr. Ahmed's cattle was 180 cows.Together they profited \$ 7800. the rent of the farm is \$ 3000 so divide the profit per gows/day for grazing day
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ihsan
from were did you get 2/50?m
People living longer
Why do you think that is?
Jazzy
because there is an increase in number of people with age more than 30.
Ok. And what do you think is the driving factor behind that hypothesis?
Jazzy
fewer birth and increase in # of years living or fewer dying
What about the improvement of technology and medicine?
Jazzy
godwin
technology and medicine is improving but they are limited
Ayunku
If those conscience of their health, one will live longer periods of life.
Montrae
hi,why the mean =sum(xi)/n but the variance =sum(xi-xbar)/ n-1 what is the difference between (n or n-1)
This is hard to type, so I'll use "m" for "x bar", and a few other notations that I hope will be clear: Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n Desired formula: sqrt((SUM[x^2] - SUM[x]^2)/n / (n-1)) Now let's do what you started to do, and see if we can manipulate the definitio
Michael
what is the difference between (n ) and (n-1) in the mean and variance
Soran
Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n what is the difference between (n and n-1)
Soran
Hi, the diference is tha when we estimate parameters in a sample (not in the total population) we need to consider the degrees of liberty for the estimation.
Nelson
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ujjal
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freakin annoying chat. uninstalled
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Abimbola
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who introduced statistics in england
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Who eats lots of food 😂
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ibrar
One who withstand everything that was meant to break him.
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