# QMS 102 Study Guide - Final Guide: Ogive, Standard Deviation, Interquartile Range

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Published on 15 Oct 2012
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Which is a better measure of Central Tendency: mean or median?
10% rule: 1) Calculate the difference A=|Mean-Median|.
2) Calculate the ―10% of the smaller of the mean and median‖, say B.
3) If A<B, then mean is the preferred measure; if A>B, then median is the preferred
measure.
mean
4615.11522x
, and median
4667
~x
. Now we apply the 10% rule:
The difference A=|
4635.6855|46674615.11522
, and the 10% of the smaller, B=10%*4667=466.7.
Since A>B, we conclude that the median is a better measure!
Mode is data entry that occurs the most
1) Arrange data in an ascending data array
Find the value
k
P
.
when r=integer,
rk xP
; when r=m+1/2,
)( 1
2
1
mmk xxP
Find the rank of the 39th percentile: n=13, k=39. So,
r = HalfRound(nk/100+1/2)
= HalfRound(5.57)=5.5
So,
3199)36462752()( 2
1
65
2
1
39 xxP
Interquartile Range = Q3 Q1
Range : Highest number of data set lowest number
For ABC Inc.,
21875.32x
and
735.6
x
s
. So, CV=
; For XYZ Inc.,
1023.32x
and
0278.6
x
s
. So, CV=
%19%100*/ xsx
. So, we can conclude that ABC Inc. has
more variability.
We can use a CASIO calculator to compute the standard deviation:
x
for the population standard
deviation, and
x
s
for the population standard deviation.
(2) To find the variance, we need to square the standard deviation.
You were asked to fill in a survey by Ryerson University about the number of courses you intend to take. One of the
questions asked is as follow: How many courses do you intend to take in the Winter 2010?
Refer to the question above being asked on the survey form. What is the measurement scale of the response data?
(a) Nominal
(b) Ordinal
(c) Interval - Continuous
(d) Ratio Discrete
(e) Ratio - Continuous
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LIF=Q1-1.5*IQR;
RIF=Q3+1.5*IQR;
LOF=Q1-3*IQR;
ROF=Q3+3*IQR
Note: (1) LIF=Left Inner Fence; LOF=Left Outer Fence;
(2) RIF=Right Inner Fence; ROF=Right Outer Fence;
(3) All data values that fall between the fences are call outliers, using ―o‖ to indicate them; All
data values that lie beyond the outer fences are call extremes, using ―*‖ to indicate them.
To measure the skewness, one can use the following:
3(mean-median)
Skewness= -----------------------------
standard deviation
1) if mean<median, then skewness<0 (negatively skewed, skewed left);
2) if mean>median, then skewness>0 (positively
skewed, skewed right);
3) if mean=median, then skewness=0 (symmetric).
. The quartiles are the values that occupy the quarter positions:
First quartile,
251 PQ
Second quartile,
502PQ
Third quartile,
753PQ
A five-number summary that consist of
Xsmallest , Q1 , Median, Q3 , Xlargest
Class Width = Highest Number - Lowest Number / 5
Right Whisker = greater than Q3 but less than RIF. Value close to RIF
Left Whisker = greater than Q1 but less than LIF . Value Close to LIF
How to calculate control limits?
Assume that we collect k samples of size n. Let
i
R
be the range of the ith sample, i=1,2,…, k. Then
)...( 1
1
1
1k
k
k
ii
kRRRR
RDUCLR4
RDLCLR3
A Normal distrubtion with mean of 0 and standard deviation of 1
Example 5. Approximate the mean of data: Height in inches.
Class frequency Middle point
5052 5 51
5355 8 54
5658 12 57
5961 13 60
6264 11 63
Solution:
041.58)11131285/)63*1160*1357*1254*851*5( x
Job classification # of employees Annual Salary (\$000’s)
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## Document Summary

10% rule: calculate the difference a=|mean-median|, calculate the 10% of the smaller of the mean and median , say b, if ab, then median is the preferred measure. mean. , and the 10% of the smaller, b=10%*4667=466. 7. Since a>b, we conclude that the median is a better measure! Mode is data entry that occurs the most: arrange data in an ascending data array. Find the rank of the 39th percentile: n=13, k=39. Range : highest number of data set lowest number. So, we can conclude that abc inc. has more variability. We can use a casio calculator to compute the standard deviation: deviation, and for the population standard deviation. for the population standard (2) to find the variance, we need to square the standard deviation. You were asked to fill in a survey by ryerson university about the number of courses you intend to take.