Percentile Handout4
2
1 MATH009 Probability and Statistics Handout # 4 Measures of Center for Grouped Data Mean n x f x i i where i i i f n i f i x frequency class th midpoint class th Median f C n w L x 2 ~ where class median the of frequency class median the before frequency cumulative than less width class class median the of boundary class lower f C w L Note: The median class is the class interval where the th n 2 observation belongs. Mode class modal the of boundary class lower L 2 1 1 ˆ d d d w L x where width class w class modal after the frequency he t and class modal the of frequency e between th difference class modal the before frequency he t and class modal the of frequency e between th difference 2 1 d d Note: The modal class is the class interval with the highest frequency. Measures of Position for Grouped Data The k th Percentile P k f C kn w L P k 100 where k k k P f P C w P L containing class the of frequency containing class the before frequency cumulative than less width class containing class the of boundary class lower Note: The class containing P k is the class interval where the th kn 100 observation belongs.
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Transcript of Percentile Handout4
1
MATH009 Probability and Statistics Handout # 4 Measures of Center for Grouped Data Mean
n
xfx
ii where
i
i
i
f n
if
ix
frequency classth
midpoint classth
Median
f
Cn
wLx 2 ~ where
classmedian theoffrequency
classmedian thebeforefrequency cumulative than less
widthclass
classmedian theofboundary classlower
f
C
w
L
Note: The median class is the class interval where the thn
2observation belongs.
Mode
class modal theofboundary classlower L
21
1 ˆdd
dwLx where widthclass w
class modal after thefrequency he t
and class modal theoffrequency ebetween th difference
class modal thebeforefrequency he t
and class modal theoffrequency ebetween th difference
2
1
d
d
Note: The modal class is the class interval with the highest frequency. Measures of Position for Grouped Data
The kth Percentile Pk
f
Ckn
wLPk100 where
k
k
k
P f
P
C
w
P L
containing class theoffrequency
containing class
thebeforefrequency cumulative than less
widthclass
containing class theofboundary classlower
Note: The class containing Pk is the class interval where the thkn
100observation belongs.
2
The kth Decile Dk
f
Ckn
wLDk10 where
k
k
k
D f
D
C
w
D L
containing class theoffrequency
containing class
thebeforefrequency cumulative than less
widthclass
containing class theofboundary classlower
Note: The class containing Dk is the class interval where the thkn
10observation belongs.
The kth Quartile Qk
f
Ckn
wLQk4 where
k
k
k
Q f
Q
C
w
Q L
containing class theoffrequency
containing class
thebeforefrequency cumulative than less
widthclass
containing class theofboundary classlower
Note: The class containing Qk is the class interval where the thkn
4observation belongs.
Measures of Variation for Grouped Data Sample Variance
1
22
2
nn
xfxfns
iiii where
i
i
i
f n
if
ix
frequency classth
midpoint classth
Sample Standard Deviation
1
22
nn
xfxfns
iiii where
i
i
i
f n
if
ix
frequency classth
midpoint classth
Example: For 80 employees of a large department store, the following distribution for years of service was obtained. Calculate the mean, median, mode, variance, standard deviation, 65
th
percentile, 1st quartile, and 4
th decile.
Class Interval Frequency 1 – 5 21 6 – 10 28 11 – 15 15 16 – 20 2 21 – 25 9 26 – 30 5
