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
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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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