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2graph_mean_sprd

# 2graph_mean_sprd - Histogram Graphs and measures of central...

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Graphs, and measures of central tendency and spread 9.07 9/13/2004 Histogram bars don’t touch. If continuous, can touch, bins. frequency”) plot Alt: for lots of bins, continuous variable, draw If discrete or categorical, should if there are lots of Sum of bin heights = N Alternative: density (or “relative Sum of bin heights = 1 histogram as a “frequency polygon” 1

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Don’t do this for categorical variables Stem-and-Leaf Plots 0755 0557 10100554 10001455 2050 ---> 2005 355 355 40 40 A quick way of examining the distribution of data Like histograms on their sides, but with more information. Data: 7 5 5 10 11 10 10 15 15 14 20 25 20 35 35 40 Stem-and-Leaf Plot: We can plot two histograms in the same plot, to compare them You get lots of distribution, but it’s kind of visually noisy. E.G. distribution of heights for women (solid) vs. men (dashed) Summarizing the distribution You might not want to look at the whole distribution in that last case. information about the shape of the Summarize. Central tendency intuition: capture the impression that the heights for the men tend to be higher than the heights for the women. 2
Measures of central tendency data, but typically only data, where the other measures we’ll discuss don’t apply. Data can have one or more modes Mode Where’s the peak of the histogram? Can be used for any used for categorical Unimodal vs. bimodal vs. trimodal Here a mode is the highest point locally Average 1 ,x 2 ,x 3 ,…,x N } mean . But note this is the sample mean . population mean . = = + + + + = N i i N x N N x x x x x 1 3 2 1 1 ... Notation: observations x={x Also known as the Soon we will talk about the Don’t get confused! Only makes sense for interval or ratio data, but will often see it used for rank-order or rating data, too 3

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Highly skewed data mode average some - where around here Negative skew. Average not at the mode. Note < 50% of data is below average Why does the average shift to the right? Average as center of mass The average gives the point where a histogram (if made of blocks) would balance. 4 0 Nov 2 Week beginning Positive or Negative Skew? % chance Earlier Nov 9 Nov 16 Nov 23 Nov 30 Later 5 10 15 20 25 30 35 Figure by MIT OCW. 100 1940 1950 1960 Year Mean number students studying Brain and Cognitive Sciences, per university 1970 1980 1990 120 140 160 180 200 220 Figure by MIT OCW.
What an outlier does to the mean right. Another measure: the median the left, ½ to the right.

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2graph_mean_sprd - Histogram Graphs and measures of central...

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