Chapter 2: Frequency Distributions - Powering Silicon Valley

1 PStem-and-leaf plot = a histogram-like display of a batch ofnumbers ( distribution )<Stem = axis = first one or two digits<Leaves = data points = next significant digit (n leaves) PIllustrative data set #1 ( , AGE variable, n = 10)<Ordered array: 05 11 21 24 27 28 30 42 50 52P Data point 21 is shown as: Chapter 2: Frequency Distributionsp. |5| |4| |3| |2|1 |1||0|AGE(x 10) Stem-and-Leaf Plot Full plot: , AGE (years, n = 10)|5|02|4|2|3|0|2|1478|1|1|0|5(x 10) 7 axis multiplier Interpretation of Stem Plotsp. (Stem-and-leaf rotated 90o) 8 7 4 2 5 1 1 0 2 0 ------------ 0 1 2 3 4 5 ------------ Age (x10)PShapePLocationPSpreadPSymmetry?

2 PMound(s)? Interpretation Shape X X X X X X X X X X ------------ 0 1 2 3 4 5 (x10) ------------Difficult to make shape statements when n smallPGravitational center (mean)<Eye-ball distribution 6 see-saw balance point 6 between 20 and 30<Exact balance point = arithmetic average = 29 PMiddle value (median)<Has depth of (n + 1) / 2< has n = 10; median has depth of (10+1) / 2 = <Average rank 5 (27) and rank 6 (28) = (27 + 28) / 2 = Central Location 8 7 4 2 5 1 1 0 2 0 ------------ 0 1 2 3 4 5 ------------ ^PRange: from 5 to 52"P Range Around Middle : 25 PMore sophisticated measures of spread in next chapterInterpretationSpread 8 7 4 2 5 1 1 0 2 0 ------------ 0 1 2 3 4 5 ------------ Age (x10)PData: third digit ( , )PPlot each point:Second Illustrative Data Set p.

3 |1|4|2|03|3|4779|4|4(x 1)PRegular plot 6 too squished to show shape, location, spread|1|4879|2|223466789|3|000123445678 (x 1)PDouble-stem values 6 does a better job showing distribution <Leaves 0 - 4 on first stem value, 5 - 9 on second|1|4|1|789|2|2234|2|68739|3|402030 41|3|8765(x 1)Third pollution levels in river water (p. )SPSSThen More on What to Look for .. p. curve SymmetryPSymmetricalPAsymmetrical<Positi ve skew: long right tail<Negative skew: long left tailPositive Negative SkewModalityp. (cont.)(A) Unimodal(B) BimodalModality = number of peaksKurtosis p. (A) Mesokurtic(B)PlatykurticC) LeptokurticLocation (p.

4 PCenter = average = summary oflocationPYou 2 Spreads(p. )Population 1 Population 2F1F2 PDeviation (F) around center as asummary PYou Can you describe thisdistribution?Exercise (%IDEAL, n = 18)| 8|8| 9|59|10|0147|11|444679|12|0145|13||14||1 5|2(% of ideal body wt x 10)Can you compare these twodistributions? Type A Men Type B Men |13|7 |14|8 |15|3 |16|9 |17|5 |18|583 7|19|4 2|20|2 28|21|23 4|22|46 4993|23| 6|24|62 240|25|52 8|26|3 6|27| |28| 1|29| |30|

5 2|31| 5|32| |33| |34|4 Cholesterol (mg/dl 10)PFrequency = no. of occurrencesPRelative Frequency = %PCumulative Frequency = no. less than orequal to current rank orderPCumulative relative Frequency = % less thanor equal to current rank orderFrequency p. p. (Example: AGE variable)AGE | Freq RelFreq. CumRelFreq ------+----------------------- 3 | 2 4 | 9 5 | 28 6 | 37 7 | 54 8 | 85 9 | 94 | 81 | 90 | 57 | 43 | 25 | 19 | 13 | 8 | 6 | 3 +-----------------------Total | 654 on no.

6 Of intervals (usually, 4 - 12)< , AGE: 05 11 21 24 27 28 30 42 50 52 <Say, 4 class intervalsPInterval width . (max min) / (no. intervals)<width . (52 - 5) / 4 = <Use practical widths, , 15-year class intervalsPSet endpoint conventions <Let s include left-endpoint and exclude right-endpoint<First interval is 0 - 14 (not 0 - 15) PCount and tabulate Grouped Data, Uniform Intervalsp. Data, Uniform Intervalsp. Tally Freq. RelFreq CumRelFreq------ ------ ----- -------- ------- 0-14 // 2 20% 20%15-29 //// 4 40% 60%30-44 // 2 20% 80%45-59 // 2 20% 100%------------------------------------ ------TOTAL 10 100% PUse , , AGENon-Uniform p.

7 (years) | Freq Percent +-----------------------PRESCHOOL (3-4)| 11 (5-11) | 469 (12-13) | 100 (14+) | 74 +----------------------- Total | 654 Freq Charts: Histogramp. 345678910111213141516171819020406080100 Other Freq Charts: Freq Polygonp. 345678910111213141516171819020406080100 Bar Charts w/ NoncontiguousBarsUse with Ordinal and Nominal GroupsAge Pre-schElem-SchMid-SchHigh-sch0100200300 400500 Group 2 FIGURES FOR TEXT