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USC / Engineering / STAT 110 / What is used for categorical variables?

# What is used for categorical variables? Description

##### Description: This study guide is a comprehensive overview of all of the information that potentially could be on Exam 2.
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Exam 2 Study Guide

## What is used for categorical variables?

∙ Chapter 10

o Quantitative Variable: a variable that measures something already in numerical  form, ex. inches of a piece of paper, weight of a person, IQ, etc.

o Categorical Variable: measures something that needs to be put into categories  and/or given numerical value, ex. favorite color, ethnicity, current feelings, etc. o Frequency table: gives the count of how many times a value appears in a  distribution, ex. 0 people like the color orange.

o Relative Frequency: gives the proportion (often a percentage or fraction) of how  many times a value appears in a distribution compared to the total amount of  values. This is often part of a frequency table.

o Pie Chart: used for categorical variables. This type of graph shows the amount of  data that belongs to each category. The categories resemble slices of a whole pie. o Bar Graph: used for categorical variables. Represents how much data is in each  category by presenting proportional bars.

## What is used for quantitative data?

o Pictogram: a bar graph that uses images instead of bars. The images must only  increase by height and NOT by width in order to be an accurate graph. o Line Graph: used for quantitative variables. This graph shows how a variable  changes over time.

▪ Look for trends (overall patterns), deviations (spikes or plunges), and seasonal variation (deviations that regularly happen) in line graph data. ∙ Chapter 11

o Histogram: used for quantitative data. This type of graph shows distribution. It  looks like a bar graph with no spaces between the bars.

o Symmetric Distribution: when the left and right sides of the graph are perfectly symmetrical.

## Define categorical variable.

Don't forget about the age old question of What is the pressure at equilibrium?

o Skewed Distribution: when one side of the graph from the center holds more  data than the other side.

▪ Skewed to the right: the right side of the graph is longer than the left side. ▪ Skewed to the left: the left side of the graph is longer than the right side. o Stemplot: essentially a histogram turned on its side that shows the exact values of  a distribution.

▪ Stem: all of the digits in a number except the last one.

▪ Leaf: the last digit in a number.

▪ Example of a stemplot: 4 | 1 2 5 8 = 41, 42, 45, 48

∙ Chapter 12

o Median (M): the middle point of a distribution when the values are in increasing  order. To find the position of the median, use the formula (n+1)/2, where n =  number of observations.

o Quartiles (Q1, Q3): divides the distribution into equal quarters when the values  are in increasing order.

▪ Q1: median (M) of smaller half of values.

▪ Q3: median (M) of larger half of values. Don't forget about the age old question of What makes a persuasion attempt successful?

▪ To find the position of the quartiles, use the same formula (n+1)/2, except  n = number of observations on one side of the median.If you want to learn more check out What is the duration of stm?
We also discuss several other topics like Costs are minimized when?

▪ If M is a number in a position (not an average of two numbers), then do  not use the median when finding the position of the quartiles

▪ If M is an average of two numbers, use the numbers that you used to take  the average when finding the position of the quartiles.

o Five-Number Summary: a list of numbers comprised of the smallest value, Q1,  M, Q3, and the largest value in a distribution.

o Boxplot: a graph of the five-number summary.

▪ For example:

25 35 45 55 65 75 85 95 105 115 125

▪ 25 is the smallest number, 45 is Q1, 65 is M, 85 is Q3, and 125 is the  largest number.

o Mean: the average of a distribution. To find the mean, use the formula (sum of  observations)/n, where n is the number of observations. Don't forget about the age old question of Define the expectancy theory.

o Standard Deviation (s): the average distance of a value from the mean. o Range Rule of Thumb: s is usually near range/4.

∙ Chapter 13

o Density Curve: shows the proportion of values in any region under the curve,  since the area under the curve equals 1.

o Normal curve: a symmetric bell-shaped curve.

▪ The mean of a normal curve identifies the center of a distribution.

▪ The standard deviation determines the shape of a normal curve.

o 68-95-99.7 Rule (Empirical Rule): in a normal distribution with a normal curve,  about 68% of the data fall within one standard deviation of the mean (34% on  either side of the mean) about 95% of the data fall within two standard deviations  of the mean (an additional 13.5% on either side of the mean), and about 99.7% of  the data fall within three standard deviations of the mean (an additional 2.35% on  either side of the mean). We also discuss several other topics like What are the sources of ethics and rituals?

o Standard score: the observations expressed in standard deviations above or  below the mean.

▪ Standard score = (observation – mean)/standard deviation.

▪ observation = (standard score*standard deviation) + mean

▪ s = the square root of the variance

o cth percentile: a value where c% of the data lie below the value.

▪ For example, at the 60th percentile, 60% of the data lie below the 60th percentile.

▪ Table B (a table in the textbook that students will be given during the  exam) gives all standard scores and their corresponding percentiles.

∙ Chapter 17

o Probability (P): a number between 0 and 1 that identifies the proportion of times  a certain outcome occurs in the long run.

o Chance behavior is unpredictable in the short run; however, chance behavior  usually has a predictable pattern after many repetitions.

o Experimental probability: exact proportion of the number of times a particular  event occurs in an experiment.

o Theoretical probability: an estimate of the proportion of the number of times a  particular event occurs when all outcomes are equally likely.

o Short-run regularity myth: phenomena that have patterns in the long run do not  need to have patterns in the short run.

o Surprising coincidence/unusual event myth: sometimes coincidences are more  likely than we think; we just need to look at the data differently.

o Law of averages: averages become more stable as the number of trials increases. o Personal probability: what a person thinks the probability of an event is. Cannot  be right or wrong since it is someone’s opinion.

∙ Chapter 18

o Probability model: identifies all potential outcomes and assigns probabilities to  those outcomes/collections of outcomes.

o Mutually exclusive events: events that have no outcomes in common. o Probability rules

▪ All probabilities fall within the range of zero and one.

▪ When all possible outcomes are added together, they should equal one. ▪ Complement rule: the probability that an event doesn’t occur = (1 – the  probability that the event does occur), aka P(Ac)= 1 – P(A)

▪ If and only if two events are mutually exclusive, then the sum of their  probabilities is equal to the probability that one or the other event occurs.  ∙ Chapter 19

o Simulation: a strategy used to figure out patterns in chance behavior when it is  not possible to perform an experiment.

o Independence: when one outcome does not affect another outcome in the same  experiment.

o When two events are independent, you can find the probability of both events  occurring by multiplying their probabilities. P(A&B) = P(A) x P(B)

∙ Chapter 20

o Expected value: the average of all possible values in the long run. o To find the expected value, multiply each outcome by its corresponding probability, and then add those numbers together.

▪ Expected value = a1p1 + a2p2 + … + akpk

o Law of Large Numbers: in a long-run experiment with many trials and  outcomes, the average of the observed outcomes approaches the expected value.

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