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Univariate data

Student learning objectives

  • The student will design and carry out a survey.
  • The student will analyze and graphically display the results of the survey.


As you complete each task below, check it off. Answer all questions in your summary.
____ Decide what data you are going to study.

Here are two examples, but you may NOT use them: number of M&M's per bag, number of pencils students have in their backpacks.

____ Are your data discrete or continuous? How do you know?
____ Decide how you are going to collect the data (for instance, buy 30 bags of M&M's; collect data from the World Wide Web).
____ Describe your sampling technique in detail. Use cluster, stratified, systematic, or simple random (using a random number generator) sampling. Do not use convenience sampling. Which method did you use? Why did you pick that method?
____ Conduct your survey. Your data size must be at least 30.
____ Summarize your data in a chart with columns showing data value, frequency, relative frequency and cumulative relative frequency.
Answer the following (rounded to two decimal places):
  1. x ¯ = _____
  2. s = _____
  3. First quartile = _____
  4. Median = _____
  5. 70 th percentile = _____
____ What value is two standard deviations above the mean?

____ What value is 1.5 standard deviations below the mean?
____ Construct a histogram displaying your data.
____ In complete sentences, describe the shape of your graph.
____ Do you notice any potential outliers? If so, what values are they? Show your work in how you used the potential outlier formula to determine whether or not the values might be outliers.
____ Construct a box plot displaying your data.
____ Does the middle 50% of the data appear to be concentrated together or spread apart? Explain how you determined this.
____ Looking at both the histogram and the box plot, discuss the distribution of your data.

Assignment checklist

You need to turn in the following typed and stapled packet, with pages in the following order:

  • Cover sheet : name, class time, and name of your study
  • Summary page : This should contain paragraphs written with complete sentences. It should include answers to all the questions above. It should also include statements describing the population under study, the sample, a parameter or parameters being studied, and the statistic or statistics produced.
  • URL for data, if your data are from the World Wide Web
  • Chart of data, frequency, relative frequency, and cumulative relative frequency
  • Page(s) of graphs: histogram and box plot

Continuous distributions and central limit theorem

Student learning objectives

  • The student will collect a sample of continuous data.
  • The student will attempt to fit the data sample to various distribution models.
  • The student will validate the central limit theorem.


As you complete each task below, check it off. Answer all questions in your summary.

Part i: sampling

____ Decide what continuous data you are going to study. (Here are two examples, but you may NOT use them: the amount of money a student spent on college supplies this term, or the length of time distance telephone call lasts.)
____ Describe your sampling technique in detail. Use cluster, stratified, systematic, or simple random (using a random number generator) sampling. Do not use convenience sampling. What method did you use? Why did you pick that method?
____ Conduct your survey. Gather at least 150 pieces of continuous, quantitative data .
____ Define (in words) the random variable for your data. X = _______
____ Create two lists of your data: (1) unordered data, (2) in order of smallest to largest.
____ Find the sample mean and the sample standard deviation (rounded to two decimal places).

  1. x ¯ = ______
  2. s = ______
____ Construct a histogram of your data containing five to ten intervals of equal width. The histogram should be a representative display of your data. Label and scale it.

Questions & Answers

what percent of the students would be expected to score above 95?
Peachy Reply
inferential statistics is what?
Seyi Reply
in which we make infrences (hypothsis)
surpose a data set of 2,3,5,6,1,4 are given find median
lucy Reply
fastest finger please
Mean (average) 4... Median (middle term) 3.5.. Mode (frequency) every element in a set has 1 frequrncy
i arrange the data set in ascending order. that is, 1,2,3,4,5,6. then find the data set that falls in the middle. in this case, 3 & 4 fall in the middle. you then sum and obtain the average. that is, (3+4)/2=3.5. therefore, 3.5 is the median.
both of you are correct.
hello guys
great to be here
how does a line graph look
pls who knows how line graph look like
line graph usually have a straight line running through axis
am new here anyone willing to orient me?
find the media of the following numbers 61,64,67,70,73
lucy Reply
my body pls
what happen to your body@hana
what is the percentile for the set of data in the class C and frequency F(c,f)given by (9.3-9.7,2) (9.8-10.2,5) (10.3-10.7,12) (10.8-11.2,17) (11.3-11.7,14) (11.8-12.2,6) (12.3-12.7,3) (12.8-13.2,1)
Chinwendu Reply
how to find median
Hrishe Reply
arrange ascending and desending order than the mid value is Median
what if it is a group data
mean/ medium/ mode
n\2 and n+1\2
An operational manager at a manufacturing company is interested in the level of satisfaction of computer buyers. The manager has developed a satisfaction scale of 1-10 to mark their level of understanding with the company.What is the population of the interest?
thomas Reply
Any clues
how to use grouped and ungrouped data
Hassan Reply
Just a test from gplay
Lucy Reply
how come 5.67
Mano Reply
by dividing 11.37 on 2
by dividing 11.34 on 2
what is index number?
What is the differences between quota an lottery system of sampling
What are the are the characteristics that are critically expedients in selecting the sample size
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
Mikki Reply
solve the question please
can some please help solve so that we learn some
It is a square chi
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
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"
sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
can't understand basic of statistics ..
Sorry I see my mistake, we have to calculate the expected values
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
why it is not possible brother
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
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
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
It is possible, sorry for my mistake
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
how to start this book, who is reading thins first time
Nissar Reply
It is my first time reading this book
Good one
from were did you get 2/50?m
Chico Reply
People living longer
Qader Reply
Why do you think that is?
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?
fewer birth and increase in # of years living or fewer dying
What about the improvement of technology and medicine?
please help me, with this.... three coins are tossed let be the number of head(h)obtain,construct a probability distribution for X
technology and medicine is improving but they are limited
If those conscience of their health, one will live longer periods of life.
hi,why the mean =sum(xi)/n but the variance =sum(xi-xbar)/ n-1 what is the difference between (n or n-1)
Soran Reply
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
what is the difference between (n ) and (n-1) in the mean and variance
Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n what is the difference between (n and n-1)
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.
Hie guys, am analysing rainfall data for different stations and i got kurtosis values of 0.7 for one station and 0.4 for another, what can i say about this?
difference in degrees of freedom

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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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