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Study Guide

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StatisticsCourse Code

STATS 250Professor

Brenda GundersonStudy Guide

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STATS 250

FINAL EXAM

STUDY GUIDE

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Lecture 1 Notes:

Slide 7:

-Sample is a subset of a larger population that we can measure

-When we summarize anything on our sample, we are calculating a statistic

-A summary measure of population data is called parameter

-A summary measure of sample data is called statistic

Slide 9:

-This is the data set we will work with today

-This data asked college kids if they are sleep deprived and how much sleep they

typically get per night in hours

-There were 86 responses on these two variables

-We want to talk about the different kinds of data we have

Slide 8:

-Can you compute the average (mean) of the amount of sleep per night for the 86

students? Yes you can

-Could you compute the average sleep deprived status of these 86 students? No. You

cannot because these are just categories. This is a different kind of variable since it

is not numerical

-Sleep deprived status is a categorical variable

-Amount of sleep is a quantitative variable (refers to numbers, able to make

averages)

-These are the two main types of variables

-Some examples of categorical vs. quantitative: Age is a quantitative variable is also

continuous), seat location is categorical, number of songs on an iPod is quantitative

is also discrete), time spent studying is quantitative (is also continuous), soft drink

size is categorical, and then… count which refers to how many times a student

says and then while telling a story is quantitative discrete

Back to slide 9:

-How would you summarize the category sleep deprived?

-You can start by counting how many people said yes and no

Slide 10:

-This is a frequency table or sometimes called a relative frequency table or

contingent table of the counts

-The number of students who said yes was 51. The remaining 35 said no

-However, you cannot use these numbers to compare to other classes that might be

bigger

-In order to do this kind of comparison, you would need to look at the percent

-For those that said yes, it is 59.3%. The ones that said no is 40.7%

-The most common representation using visual is a bar graph

-For bar graphs in general, we will not use words or describers like skewed to

show the shape or things such as increasing trend

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-These words are used for other graphs when we talk about a quantitative variable,

not a categorical one

-We can’t do much with categorical data

Slide 11:

-For categorical variables, we will prefer to look at bar charts

-Now we will look at the quantitative variable, which was the amount of sleep, they

get per night

-Instead of summing up all the variables (which can be a lot), you can find the

smallest and largest value

-In this case, the smallest value is 1 hour and the largest value is 11 hours

-Now we’ll take that overall range and break it up into intervals of equal width

-For this, we can go by 2 (its up to you) but pay attention to the endpoints

Slide 12:

-We will set up a frequency table for the values but not for each individual value;

rather, classes of values

-The first category will be a bracket meaning that value (in this case it is a 0) will be

included in the count and the next value will be closed as well

-However, from there on, the first value will be in parenthesis while the second

value is in brackets

-This will continue until you reach the end

-Make sure you don’t double count one of the variables

-Frequency (top to bottom): 1, 2, 12, 56, 14, 1. These all add up to 86

-Relative frequency or proportion (divide the frequency by 86): 0.012, 0.023, .139,

.651, .163, .012. These should add up to 1

-Simply convert to percent by multiplying by 100 and they all should add up to a

100%

-Do 4 significant figures for your answers

-A nicer way to see this data is through the use of a histogram

-The x-axis will be amount of sleep in hours (spaced out with the amount we used

before which was 2)

-Y-axis is the count

Slide 13:

-What can we interpret from these graphs?

-We can look for overall pattern (shape, location, spread)

-We can look for deviations from overall pattern (outliers)

Slide 14:

-First thing we will talk about is what is the overall pattern when you look at a

histogram

-For that, we will talk about shape, location and spread

-The first graph to the left is called symmetric and somewhat bell-shaped

-The one below it is also symmetric but not bell-shaped. It is called uniform because

it is equally likely over that whole range

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