 # Chapter 1 – Exploring Data YMS - 1.1 Displaying Distributions with Graphs xii-7.

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Chapter 1 – Exploring Data YMS - 1.1 Displaying Distributions with Graphs xii-7

Consider This…. Data beat anecdotes - seatbelts Lurking variables – Simpson’s Paradox Origin of data – Ann Landers Variation 3 W’s – Who, What, Why? xii-7

Vocabulary Data Numbers with a context Numbers with a contextIndividuals Objects described by a set of data Objects described by a set of dataVariable Characteristic of an individual Characteristic of an individual Categorical Variable – places individual into one of several groups or categories Quantitative Variable – take values for which arithmetic operations make sense xii-7 p7 #1.1 – 1.4

Case Row of data (all variables of an individual) Row of data (all variables of an individual)Distribution Pattern of variation of a variable Pattern of variation of a variable What values the variable takes and how often What values the variable takes and how often Exploratory Data Analysis Statistical tools and ideas that help you examine data in order to describe their main features Statistical tools and ideas that help you examine data in order to describe their main features xii-7

CountPercentOutlier Overall Pattern of a Distribution (SOCS) Shape. Outlier. Center. Spread. Shape. Outlier. Center. Spread. Write 2-3 sentences in context with appropriate measures. Write 2-3 sentences in context with appropriate measures. 8-17

Types of Graphs 1.Bar Graph Leave a space between the bars Leave a space between the bars Label the category names at equally spaced intervals beneath the horizontal axis Label the category names at equally spaced intervals beneath the horizontal axis 2.Pie Chart Must add up to 100% Must add up to 100% Let the computer create it Let the computer create it 3.Dotplot Mark a dot above number on horizontal axis corresponding to each data value Mark a dot above number on horizontal axis corresponding to each data value 8-17

4.Stemplot Stems and leaves are arranged in increasing order Stems and leaves are arranged in increasing order Include legend Include legend Split stems if necessary (0-4 and 5-9) Split stems if necessary (0-4 and 5-9) Round or truncate when necessary Round or truncate when necessary p15 Technology Toolbox Greed 8-17

The Game of Greed Everyone stands. A pair of dice will be thrown by a classmate. After each toss you have the option to sit and keep the score (the total on the dice) or stand and continue onto the next round. The game is over when everyone has decided to sit OR when a two is thrown (not snake eyes - just the number 2). If you're standing when a 2 is thrown, your score for the round is zero. A game consists of 5 rounds. At the end of the game, add your 5 scores to get your total. HW: p16 #1.8 & 1.9

Activity: Legendary WS More Vocab Symmetric If the right and left sides of a distribution are mirror images of each other If the right and left sides of a distribution are mirror images of each other Right/Left Skewed Values are stretched to the right/left Values are stretched to the right/leftPercentile The value such that p percent of the observations fall at or below it The value such that p percent of the observations fall at or below it 18-34

5.Time plots Plots each observation against the time at which it is measured Trend - a long-term upward or downward movement over time Seasonal Variation - a pattern that repeats itself at regular time intervals 18-34 More Graphs

6.Histogram Graphs the distribution of one quantitative variable Graphs the distribution of one quantitative variable Precise intervals Precise intervals Intervals must be kept at same width Intervals must be kept at same width Can use percentages instead of counts Can use percentages instead of counts 18-34 p22 #1.12 – calculator – zoom stat p27 #1.16 – reading a histogram

7.O-Jive aka Relative Cumulative Frequency Graph Make table with class, frequency, relative frequency, cumulative frequency, and relative cumulative frequency Make table with class, frequency, relative frequency, cumulative frequency, and relative cumulative frequency Plot a point corresponding to the relative cumulative frequency in each class interval at the left endpoint of the next class interval Plot a point corresponding to the relative cumulative frequency in each class interval at the left endpoint of the next class interval p31 #1.19 18-34 HW: #1.20, 1.26 & 1.28 Meet in the lab 557 tomorrow.

YMS - 1.2 Describing Distributions with Numbers

Measures of Center Mean Add all values and divide by the number of observations Add all values and divide by the number of observations Not a resistant measure of center Not a resistant measure of centerMedian Midpoint of a distribution; 50th percentile Midpoint of a distribution; 50th percentile All values must be arranged in increasing order before finding median All values must be arranged in increasing order before finding median Median is a resistant measure Median is a resistant measure Mean vs. Median When to use When to use In skewed distributions In skewed distributions #1.34-1.35 on p41 37-47

Range Difference between largest and smallest value of a distribution Difference between largest and smallest value of a distributionQuartiles 25th and 75th percentiles 25th and 75th percentiles Interquartile Range The distance between the first and third quartiles The distance between the first and third quartiles Modified Boxplots Shows the outliers Shows the outliers Always use this one! Always use this one! 37-47 Boxplots and Vocab

Outliers 1.5 x IQR Rule 1 3 3 5 7 10 11 11 11 15 25 #1.36 on p47 #1.39 on p48 37-47

Measures of Spread Standard Deviation How far are the observations from their mean How far are the observations from their mean The larger the standard deviation, the wider the distribution The larger the standard deviation, the wider the distribution Is the square root of the variance Is the square root of the variance Is not a resistant measure Is not a resistant measureVariance Average of the square of the deviations of the observations from their mean Average of the square of the deviations of the observations from their mean Has a different unit of measurement than standard deviation Has a different unit of measurement than standard deviation #1.40 and #1.43 on p52 49-53

Degrees of Freedom = n -1 What measures to use Mean and Standard Deviation Mean and Standard Deviation Reasonably symmetric distributions that are free of outliers 5-number summary 5-number summary Skewed distributions or ones with strong outliers Would you rather have a 10% raise or a \$1000 raise? 49-53

Effect of a Linear Transformation x new = a + bx Fathom First Day Multiplying by constant b Multiplies both measures of center and spread by constant b. Multiplies both measures of center and spread by constant b. Adding the same number a Adds a to measures of center and to quartiles Adds a to measures of center and to quartiles Does not change measures of spread Does not change measures of spread Transformations do not change the shape of a distribution 53-66

Use back to back stemplots or boxplots Easy to do in Fathom! Example 1.17 on p57 Comparing Distributions 53-66

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