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Lecture 4

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Department
Quantitative Methods
Course
QMS 102
Professor
Sheila Rosenberg
Semester
Fall

Description
Alyssa Soubliere Ryerson University September 30, 2013 QMS102 Lecture 4 Lecture4Notes Ogive Tips  To plot an ogive construct the vertical axis (y-axis) representing the c% and the horizontal axis (x-axis) representing the upper boundary for each class interval  Start the graph at the first boundary  Plot all points (upper boundary, c%) and connect them with line segments  The rules for plotting an ogive apply to any cumulative relative frequency distribution. Even if there are classes of unequal width or open ended classes Find Percentage and Annual Sales:  To find the percentage less than 80000 go vertically upward at 80 of the x-axis until you hit the ogive. The y-value is 65%. So, 65% of the total 78 products is 65/100 * 78 = 50.7  100-84 for annual sales ... do not need to multiply by 100 as it is already in a percentage Measure of Location  A percentile is the value below which a certain percent of observation fall th  The symbol for percentile is Pᵏ = k percentile  The k percentile in a data set is the value for which k% of the data are smaller than the value and (100-k) % Steps to Measure of Location: Step One: Arrange the data into ascending array Step Two: Calculate the rank of the k percentile using the following formula: R= Rank of Pᵏ = Half Round [n * (k/100) + (1/2)] Step Three: Computer Pᵏ  If the rank is an integer Pᵏ = xᵣ  If r is 0.5 you use the number on both sides (0 and 1) o “fractional half” Notation  N= number of observations  K = % of observations less than or equal to Pk  The function Half Round (x) rounds the non-integer to the nearest half o Half round (2.3) = 2.5, Half Round (3.8) = 4, Half Round (7.7) = 7.5 o Round 0.25 and 0.75 down is k < 50 Alyssa Soubliere Ryerson University September 30, 2013 QMS102 Lecture 4 o Round 0.25 and 0.75 up is K > 50 o For example: if k = 25, then half round (4.25) = 4 o For example if k = 75, then Half Round (4.25) = 4.5 Quartiles Some percentiles have special names:  First Quartile = Q1 = 25 percentile th  Second Quartile = Q2 = 50 percentile  Third Quartile = Q3 = 75 percentile  The Casio calculator “calc” gives Q1, Q2, and Q3. If you need to find any other percentile you must use the formula.  Quartiles – Example 1: X= 4, 6, 8, 12, 20 Since Q1 = 25 percentile = P25 we have k = 25 therefore: R= half-round [5 * (25/100) + (1/2)] = half round (1.75) = 1.5 Since the decimal ends with a .75 and k is less than 50, round down to 1.5 Data Rank: The rank r= 1.5. So we take the average q1 = p25 = (x1 + x2)/2 = (4+6)/2
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