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Chapter 3 notes

# Chapter 3 notes - Chapter 3 Elementary Descriptive...

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Chapter 3 – Elementary Descriptive Statistics Given precise enough measurement, even supposedly constant process conditions produce differing responses. For this reason we are not as interested in individual data values as we are in the pattern or distribution of the data as a whole. Section 3.1: Elementary Graphical & Tabular Treatment of Quant. Data Dot Diagram and Stem-and-Leaf Plots Example 3.1 : The government requires manufacturers to monitor the amount of radiation emitted through the closed door of a microwave. The following are radiation amounts emitted by 24 microwaves measured by one manufacturer. .01 .08 .05 .11 .02 .12 .08 .03 .10 .07 .10 .05 .10 .20 .01 .09 .05 .09 .02 .10 .18 .20 .30 .15 It is easiest to first order your data: .01 .03 .07 .09 .10 .18 .01 .05 .08 .10 .11 .20 .02 .05 .08 .10 .12 .20 .02 .05 .09 .10 .15 .30 Dot Diagram Stem-and-Leaf Plot – we use the first digit after the decimal place as the “stem” and the second as the “leaf” 1

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-When there are too many observations appearing on one stem, we can split each stem into two. This can help produce a stem-and-leaf plot that gives a better indication of the distribution of the data. Other examples of splitting data into stem and leaf: Data Stem and Leaf for first observation 65, 70, 62, 56, … treat 6 as the stem and 5 as the leaf, etc. 2.6, 2.8, 3.1, 4.5, … treat 2 as the stem and 6 as the leaf, etc. 58.65, 62.87, 60.15, 59.72, … treat 58 as the stem and 65 as the leaf, etc. Back-to-back stem-and-leaf plots can be used to compare two data sets: Frequency tables and Histograms For frequency tables, we use intervals of equal length, but the number of intervals we use varies and is a matter of judgment. We also want to make sure that the endpoints of the intervals are set such that every data point is included in exactly one interval. Guidelines for making Histograms: Use intervals of equal length, show the entire vertical axis beginning at zero, avoid breaking either axis, keep a uniform scale across a given axis, and center bars of appropriate heights at the midpoints of the intervals. Example 3.1 continued: Frequency Table 2
Histogram Some common distributional shapes that we can identify through the above graphical techniques: Bell-shaped or Normal Left-skewed (tail at left) Right–skewed (tail at right) Uniform Bimodal Truncated Scatterplots and Run Charts Example 3.2 : Scatterplot for ACT score and Highschool GPA for 12 students ACT 24 27 18 16 20 22 23 18 17 19 31 27 GPA 3.3 3.8 1.8 2.1 2.6 2.7 3.1 2.6 2.0 2.5 4.0 3.5 The scatterplot of GPA against ACT score shows a fairly strong positive linear relationship.

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