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Get Full Access to Clemson - STAT 3090 - Class Notes - Week 4
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CLEMSON / Statistics / STAT 3090 / What is relative frequency and cumulative frequency?

What is relative frequency and cumulative frequency? Description

Description: These notes cover material from class during week 3 and week 4.
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Chapter 2 Notes

What is relative frequency and cumulative frequency?

• Deviation—Given a value y and a data point x then x-y represents  how far x deviates from y.

o Ex. Given x=10 and y=5.  10 deviates by 5 from 5.

• Bar Charts—Display where the length of a bar corresponds to the  frequency or number of observations in a category

• Pie Charts—Slice is proportional to the amount in each category  • Relative Frequency—The proportion and is calculated by relative  frequency= # in the class/# total.

• Cumulative Frequency—Sum of frequencies of a particular class  and all preceding classes.

• Cumulative Relative Frequency—Make the cumulative frequency  relative.

How do you arrange data in an array?

• Histogram—A bar graph of frequency or relative frequency • Algorithm

1. Determine the number of classes

2. Find the smallest and largest value

3. Class Width=largest – smallest divided by total number of  classes

4. First class is usually the first class with the smallest number  and starting at a multiple of the class width

5. Find class boundaries are the average/midpoint between  two classes

a. Lower class boundary < xi < upper class boundary 6. Calculate the frequency or relative frequency

7. Create a bar graph!

***Class boundaries are sometimes called cut points.  Classes are  sometimes called bins.

• Ordered Array—List of all data points in order

How do you calculate a weighted mean?

Don't forget about the age old question of How does variety of lean protein affect eating pattern?

o Rank order: increasing order

o Reverse rank order:  decreasing order

• Dot Plot—Graph where each data point is a point above a  horizontal axis (usually a number line) if multiple entries have the  same value they are stacked

• Probability Distribution—Assigns a probability to a set of possible  outcomes

• Symmetric Distribution—If one were to draw a line down the  middle of the distribution the two sides would mirror each other • Skewed (asymmetrical) Distribution—Not symmetric or a group  of observation that are not equal on both sides

1. Left Skewed—Left side longer

2. Right Skewed—Right side longer

• Unimodal—Distribution has each one “peak”

• Bimodal—Has exactly two “peaks”

• Multimodal—Has more than one “peak”

• Mode—The value that occurs most frequently, not necessarily  unique

• Mean—The average

o Sample Mean—Xi is the data point in a sample

o Population Mean—N is the number of elements in the  population.  For a finite population.

o Weighted Mean—Suppose the ith observation is given a  weight wi We also discuss several other topics like What happened in the chesapeake incident?

o Trimmed Mean—Ignores equal percentages of the highest  and lowest data points.

• Median—Data value in the center of an odered list o Ex. 1,3,4,6,3,4,5—1,3,3,4,4,5,6.  4 is the median.

• Outlier—Data points that are extremely small or large relative to  the data set.

• Resistant—Statistics not affected by outliers are called resistant • Range—The difference between the largest and smallest value • Empirical Rule—Derived from a bell-curve (normal distribution) We also discuss several other topics like What makes potassium flouride ionic?

o One-sigma rule—68% of data lives within one standard  derivation of the mean

o Two-sigma Rule—95% of the data lives within 2 standard  deviations of mean  If you want to learn more check out How do you solve a lagrangian equation?

o Three-sigma—99.7% lives within 3 standard deviations of  the mean

• Chebyshev’s Theorem—Proportion of any data set lying within K  standard deviations of the mean is at least 1-1/k2 for k>1 • Percentiles—Given a set of data xi,…xN, the Pth percentile is a  value, say x, such that approximately P% of the data is less than or  equal to x and (100-P)% is greater We also discuss several other topics like What was the dominant form of political organization?

• Percentile of a Value—Percentile of x=#data pts. =x/total # of  data pts.

• Quartiles—The 25th 50th 75th percentiles are the first, second, and  third quartiles Q1, Q2, Q3

• Interquartile Range—Difference between third and first quartile • Outliers—A data point is considered an outlier if it is 1.5 times the  IQR above Q3 or 1.5 times the IQR be between Q1

• Z-score—The number of standard deviations x away from the  mean.

• Mean of Grouped Data—Data points might be binned in classes • Random Experiment—An activity or event where the outcome is  uncertain

• Sample Space—The set of all distinct outcomes of an experiment  • Relative Frequency—Rel Freq. of A=# times A occus divided by  the # times of the experiment We also discuss several other topics like How does social class influence families?

• Set Theory—A set is a list without repeats

o Compound event:  A combination of two or more events o Union of Events:  A & B is the set of outcomes that are  included A or B or both.  Denoted AυB

• Intersection—Intersection of events A & B is the set of all  outcomes that are in both A & B.

• Complement of Event A—the set of all outcomes not in A • Mutually Exclusive—The two sets A and B are mutually exclusive  if they have no points in common

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