Lecture 8/Chapter 7 Finding Data in Life (completed): 1. - PowerPoint PPT Presentation

Course Divided into Four Parts (Review) Lecture 8/Chapter 7 Finding Data in Life (completed): 1. scrutinizing origin of data Part 2. Summarizing Data Finding Life in Data: summarizing data 2. Ch.7: Measurement Data yourself or assessing another’s summary Understanding Uncertainty in Life: 3. � Summaries probability theory � Displaying with Stemplots Making Judgments from Surveys and � Displaying with Histograms 4. Experiments: statistical inference Definitions (Review) Definitions � Variable : a characteristic that varies from one Summarize values of a quantitative (measurement) individual to another variable by telling center, spread, shape. � Statistics: the science of principles and � Center : measure of what is typical in the procedures for gaining and processing data distribution of a quantitative variable (info about variables’ values for a sample) and � Spread: measure of how much the using the info to draw general conclusions distribution’s values vary � Statistics: summaries of data (such as a � Shape: tells which values tend to be more or sample average or sample proportion) less common

Example: Basic Summaries Definitions Measures of Center � Background : Cigarettes smoked in a day for sum of values 22 smoking students: � mean= average= number of values 1 2 4 5 7 10 10 10 10 12 15 � median: 15 15 20 20 20 20 20 20 20 25 30 � the middle for odd number of values � Question: How can we summarize the data? � average of middle two for even number of values � Response: � mode: most common value 1. center Measures of Spread mean (average) = � � Range: difference between highest & lowest median = middle: � � Standard deviation (discussed later) mode (most common) = � Example: Basic Summaries Definitions for Shape � Symmetric distribution : balanced on either � Background : Cigarettes smoked in a day for side of center 22 smoking students: 1 2 4 5 7 10 10 10 10 12 15 � Skewed distribution: unbalanced (lopsided) 15 15 20 20 20 20 20 20 20 25 30 � Skewed left: has a few relatively low values � Question: How can we summarize the data? � Skewed right: has a few relatively high values � Response: � Outliers: values noticeably far from the rest 2. spread (variability): range is � Unimodal: single-peaked 3. shape: � Normal: a particular symmetric bell-shape

Displays of a Quantitative Variable Definition Displays help us see the shape of the distribution. � Stemplot: vertical list of stems, each followed by horizontal list of one-digit leaves � Stemplot Advantage: most detail stems 1-digit leaves � Disadvantage: impractical for large data sets � � Histogram . Advantage: works well for any size data set � . . Disadvantage: some detail lost � � Boxplot � Split stems: If plot has too few stems, split Advantage: shows outliers, makes comparisons � into 2 (1st stem gets leaves 0-4, 2nd gets 5-9) Disadvantage: much detail lost � or 5 (1st stem gets leaves 0-1, etc.) or 10. Example: Basic Stemplot Example: Splitting Stems Background : Earnings of 29 male students: Background : Cigarettes smoked in a day for 22 � � smoking students: 0 2 2 3 3 3 3 4 4 5 5 5 5 5 5 1 2 4 5 7 10 10 10 10 12 15 6 6 6 6 7 8 8 10 10 12 15 20 25 42 15 15 20 20 20 20 20 20 20 25 30 Question: Construct stemplot, describe shape? Question: Construct stemplot, describe shape? � � Response: start with 0 to 4 as stems: � Response: � Almost all the values would appear in 0 0 2 2 etc. the first line, resulting in a poor display. 1 2 3 4

Example: Splitting Stems Definition Histogram: to display quantitative values… 0 2 2 3 3 3 3 4 4 5 5 5 5 5 5 � 6 6 6 6 7 8 8 10 10 12 15 20 25 42 Divide range of data into intervals of equal 1. Response: split stems in 2: � width. 0 Find count or percent or proportion in each. 2. 0 Use horizontal axis for range of data values, 1 3. 1 vertical axis for count/percent/proportion in Note: mean=___median=___th value=___range__ to__. 2 each. 2 Shape is___________________ (picture it rotated to horizontal orientation with 0 at left, 4 at right); 3 Outliers? 3 4 Example: Histogram Example: Another Histogram Background : Earnings of 29 male students: Background : Earnings of 47 female students: � � 0 2 2 3 3 3 3 4 4 5 5 5 5 5 5 0 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 5 5 5 7 7 8 8 8 10 12 15 17 18 25 26 34 6 6 6 6 7 8 8 10 10 12 15 20 25 42 Question: Make histogram with midpoints 0, 5, etc? Question: Make histogram with cutpoints 0, 5, etc? � � Response: Response: (Note that stemplot would be tedious.) � � Center: mean=____ Note: same shape median=____th value=___ as seen in stemplot. Spread: values range from ___ to ___ Shape: Similar to males’ shape?