Group Members: Charlie, Tyler, Renzheng
Chapter 1 Review:Exploring Data
Analyze data by using graphs and numerical summaries
Use graphs to display categorical or quantitative data
Describe the overall pattern by interpreting shape, center, spread, and outliers (SOCS)
Choose a which center and summary best fits the data. (mean and deviation or five-number summary)
Determine the effect of a linear transformation on center and spread
The Big Idea
Model of the Big Bang
Individuals – are the objects described by the data. Can be people or things
Variables – are any characteristics of an individual
Categorical variables - places an individuals into groups or categories
Quantitative variables – takes numerical values like 2 or 4.5
Distribution – of a variable tells us what values the variable takes and how often it takes these values
Vocabulary You Need to Know
Graph categorical data on pie charts and bar graphs. Graph quantitative data on stemplots and histograms,
Ogive or relative cumulative frequency graphs and timeplots are quantitative
Describe Shape: symmetric or skewed, unimodal or no modes
Describe Center: Mean or Medium. They are the same in symmetric but in a skewed, the mean is farther out than the median near the tail
Describe Spread: range, quartiles, five number summary, standard deviation
Outliers: Median and quartiles are resistant. Mean and Std deviations arnt
Key Topics Covered in this Chapter
Mean
Variance
Standard Deviation
Outliers smaller than Q1 – (1.5 *IQR) or larger than Q3 – (1.5*IQR)
Linear transformation xnew = a + bx (a shifts values up or down, b changes the size)
Five number summary (min, Q1, medium, Q3, max)
Range = maximum – minimum
Formulas You Should Know
Enter data into L1 and L2 then press 1-var stat under calculations.
This will find the mean and standard deviations.
Remember the difference between (s) sample and (σ) population
Calculator Key Strokes
Use back to back stemplots and side by side boxplots are used to compare quantitative distributions
Use mean and standard deviation for symmetric and Normal distributions and the five number summary for skewed distributions
The sum of all deviations from their mean will always be 0. s = 0 only when all observations have the same value
The number n – 1 is called the degrees of freedom of the variance or std. deviation
Average value refers to the mean and typical value to the medium
Histograms should always have bins of the same size and the bars touch each other
Helpful Hints
-799, 0, 4, 32, 54 ,93, 354, 354, 1534, 3942, 4032, 5030
a) Find the Five number summary
b) Find any outliers
c) Find the mean and standard deviation
d) Make a boxplot and a histogram
e) Describe SOCS
a) (-799, 43, 86, 2738, 5030)
b) None
c) Mean = 1219.1666 std dev. = 1965.9759
d)
e) Skewed, no outliers, medium, quartiles
Example Problem(s)
Top Related