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STAB22H3 (239)
Ken Butler (34)


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Ken Butler

STAB22 LEC04 (Covers entire chapter 5, and some beginning part of chapter 6) ---------------[CHAPTER5]----------------- Note - near the end of the lecture, he discusses data about potassium. He is getting that data from: --------------------------------- [36] CHAPTER 5: UNDERSTANDING AND COMPARING DATA Data val's - 10,11,14,15,17,19,21,28,35 Find: a) median = 17 b) Q1= 14 c) Q3 = 21 d) IQR = Q3 - Q1 = 21 - 14 = 7 e) max = 35 f) min = 10 5-Number Summary - gives min, Q1, median, Q3 and max: => 10, 14, 17, 21, 35 - summarizes the extremes, and the percentiles (25th, 75th, 50th) => capable of summarizing large quantity of #'s w/ small quantity of summary val's (only 5) - Note - 50th percentile aka median [37-38] BOXPLOT - visual display retireved from using the following statistical summaries: - median, Q3, Q1, min, max, upper fence, lower fence, and IQR => incorporates 5-number summary in a visual display - scale on left Calculating the "fences" - these are imaginary horizontal lines at particular values  upper fence - UF = Q3 + (1.5)(IQR)  lower fence - LF = Q1 + (1.5)(IQR) - Note - he expressed "R" to equal (1.5)(IQR). So, we can alternatively write the UF, LF formulae as follows: - UF = Q3 + R - LF = Q1 + R - draw vertical lines protruding from box of boxplot to most extreme value WITHIN THE FENCES - if there is a val. that is OUTSIDE the fence, plot it individually - these are SUSPECT OUTLIERS P37 BOXPLOT R Recall: ----------- - UF = Q3 + R - LF = Q1 + R , where R = (1.5)*(IQR) ----------- - R is a determinant value for whether a value is too big, or too small, and thus should be considered an outlier - the explanation for why it we multiplied IQR by 1.5 - the professor says "B/c it is." - if we picked greater than 1.5, then value has to be very very big to be considered "suspicious" - ath about upper or lower fence is suspiciously large or suspiciously small Data val's - 10,11,14,15,17,19,21,28,35 - largest: 35, bigger than upper fence - smallest: 10, which isn't smaller than smaller fence, which was 3.5, Further notes on Boxplot - all that matters in the v.axis => hrztal scale (aka x-axis) doesn't mean ath at all => how wide the boxplot is does not matter, and does not mean ath With respect to our example - dot - largest val - out, beyond the fence (in this ex., it is beyond UF) - we draw atn to it b/c it is unusually large Advantages of Boxplot - upon seeing it, you get immediate picture of centre and spread of data - centre instantly (often times) from line in middle, which is median - height of box is Q3 - Q1, which is IQR - the taller the box is, the more spread out data val's are - if box taller, IQR bigger b/c Q3 and Q1 more farther apart - unlike histogram or stem plot, it gives you centre and spread directly, and tells you about unusually high or low val's Example: 35 - high val = 35 - do further investigation questioning if 35 is correct - an outlier ------------------------- MyStatCrunch instructions - Graphics -> Boxplot -> select column - "use fences to identify outliers" - Otherwise it will show whiskers all the way to top, all the way to bottom ------------------------- [39] COMPARING DISTRIBUTIONS WITH BOXPLOTS - ex - classify cereals on which shelf they are, and do they differ in the amt of sugar they have per serving - compare these three distributions - commonality: each measures sugar serving of cereals - difference: the cases are in a particular shelf - ie. for "1", only counts cases (ie. cereals) on top shelf - ie. for "2", only on middle shelf - ie. for "3", only on bottom shelf [40] Comparing the 3 distributions with Histograms - hard to look at and compare - have to also decide where middle of distributions are, which is not easily found using this display [41] Comparing the 3 distributions with Boxplots - instead do side-by-side box plots => more clearer story from that - used to compare var's or var's grouped up in diff. ways Shelf 1 - median at around 4 (line on mid of box) - whiskers - bottom one short, top one long => appear to be skewed to right - no outliers, b/c no pts plotted by themselves - Q1 to bottom of data - not v.far - Q3 to top of data - data quite spread out Shelf 3 - around 7 for median - whiskers about same length top and bottom => distribution is roughly symmetric Shelf 2 - where is median? - There is no line across the box somewhere in the middle => median must be same as Q1 or Q3 - longer whisker at bottom => distribution appears to be skewed to left Advantages of Boxplot - gives quick comparison of distributions if want to know what certain statistical summary is (given that is is displayed by boxplot) - ex. could easily compare medians for sugar count b/ween the three distributions - comparing diff. groups for sth is done best by comparing box plots side-by-side - ex. cereals on diff. shelves - comparing length of upper whisker to bottom whisker within one distribution, and b/ween distributions to get an idea as to direction of skewedness, if any - both similar/same lengths => symmetric - upper whisker longer => skewed to right - lower whisker longer => skewed to left [42] Where is median for shelf 2? - median = Q3 - likely b/c there are a lot of cereals that have sugars exactly 12 - b/c so many
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