Transcription of Describing Data: Frequency Distributions, and Graphic ...
1 Describing Data: Frequency Distributions, and Graphic presentation The McGraw-Hill Companies, Inc. 2008 McGraw-Hill/IrwinChapter 2 Constructing a Frequency distribution Step 1: order data Step 2: The number of classes(k). A useful rule 2 to the k rule. such that2k> n, (n # of data )22> n, (n # of data ) Step 3: The class interval (i) or width. i (H-L)/k, i: interval, H: highest value, L: lowest value Step 4: starting value<=L, L:lowest value Step 5: make class and Frequency by starting from L then increase i and stop when you get k and count Frequency in each : The prices of 7 cars sold last week are: 5, 7, 5, 15, 12,7,8 Construct Frequency ditribution Solution:1. order(5,5,7,7,8,12,15) 2. then k=33.
2 Interval (i): H=15, L=5 then7823>= = i3. interval (i): H=15, L=5 then4. Starting value=L=5 5. Frequency = i# of cars ( Frequency )Price (class)55 up to (<) 919 up to (<) 13113 up to (<) 17 7 Total Midpoint (M) The midpoint is halfway between the lower limit and upper limit in each class. Example: find the midpoint for this table:4 MFrequencyPrice(5+9)/2=755 < 9(9+13)/2=1119 < 13(13+17)/2=15113 <17 7 TotalRelative Frequency DistributionTo convert a Frequency distribution to a relative Frequency distribution , each of the class frequencies is divided by the total number of observations. ff5 Graphic presentation of a Frequency DistributionThe two commonly used Graphic forms are:6are: Histograms Cumulative Frequency distributionsHistogramHistogram The classes are marked on the horizontal axis and the class frequencies on the vertical axis.
3 The class frequencies are represented by the heights of the Frequency Distribution8 Cumulative Frequency Distribution9 Example: From previous graph answer the following: How many vehicles sold: 80 What is class interval: for example: 21-18=3 Estimate median: median (Q2) at 50% or p=50 then from Estimate median: median (Q2) at 50% or p=50 then from the graph about $ How much selling 25 or less vehicles:about $20 What percent of vehicle their prices $ or less:about 88% Estimate inter-quartile range:IQR=Q3-Q1=26-19=7 where Q3:third quartile(75%,p=75), Q1:first quartile(25%, p=25)10 End of chapter 211 End of chapter 2
