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)