using formulas that contain relative frequency (p) instead of frequency (f)


relative frequency

frequency divided by total frequency

relative frequency

accumulate relative frequency

accumulate frequency divided by total frequency

accumulate relative frequency

table example

accumulate relative frequency relative frequency weight
accumulate relative frequency relative frequency X
0.125 0.125 40-50
0.25 0.125 50-60
0.5 0.25 60-70
0.68 0.18 70-80
0.8 0.12 80-90
0.9 0.1 90-100
0.96 0.06 100-110
1 0.04 110-120
1


mean



developing formula from previous formulas the end formula is right side

developing  mean formula according to relative frequency

multiplication of relative frequency and mid point of the class accumulate relative frequency relative frequency mid point of the class in case of continuous variable weight
xi · pi accumulate relative frequency relative frequency Xi X
5.625 0.125 0.125 45 40-50
6.875 0.25 0.125 55 50-60
16.25 0.5 0.25 65 60-70
13.5 0.68 0.18 75 70-80
10.2 0.8 0.12 85 80-90
9.5 0.9 0.1 95 90-100
6.3 0.96 0.06 105 100-110
4.6 1 0.04 115 110-120
mean  =  72.85 <= sigma xi pi סכום המכפלה של השכיחות היחסית ואמצע טווח הנתונים 1






variance



formula developing from previous formulas the end formula is right side

developing  variance formula according to relative frequency




multiplication of relative frequency and mid point of the class accumulate relative frequency relative frequency mid point of the class in case of continuous variable weight
Xi^2·Pi accumulate relative frequency relative frequency Xi X
253.125 0.125 0.125 45 40-50
378.125 0.25 0.125 55 50-60
1056.25 0.5 0.25 65 60-70
1012.5 0.68 0.18 75 70-80
867 0.8 0.12 85 80-90
902.5 0.9 0.1 95 90-100
661.5 0.96 0.06 105 100-110
529 1 0.04 115 110-120
------ ------
5660 sum 1





   352.88 =  5660-72.85^2 =  developing  variance formula according to relative frequency = variance   





median


formula developing from previous formulas the end formula is right side
the median group contain the member 0.5
the median in position 0.5

developing  median formula according to relative frequency


accumulate relative frequency  -  accumulate frequency up to the median group , the median group is not include

L-the lower limit of the median group

C-the width of the median group

relative frequency  -  relative frequency of the median group


median group accumulate relative frequency relative frequency weight
med accumulate relative frequency relative frequency X
0.125 0.125 40-50
0.25 0.125 50-60
0.5 0.25 60-70
=> 0.68 0.18 70-80
0.8 0.12 80-90
0.9 0.1 90-100
0.96 0.06 100-110
1 0.04 110-120
sum 1



70 = med = 70 + ((0.5-0.5)/0.18) · 10

mode


regular mode formula

mode

L - the lower limit of the mode group

density difference between the mode group to the group  before  -  the density difference between the mode group and the group before

density difference between the mode group to the group after  - the density difference between the mode group and the group after

C - the width of the mode group



relative frequency formula

developing  mode formula according to relative frequency


the mode group there is the group with the highest density

developing  median formula according to relative frequency

mode group relative frequency group width accumulate relative frequency relative frequency weight
mode relative density c accumulate relative frequency relative frequency X
0.0125 10 0.125 0.125 40-50
0.0125 10 0.25 0.125 50-60
=> 0.025 10 0.5 0.25 60-70
0.018 10 0.68 0.18 70-80
0.012 10 0.8 0.12 80-90
0.01 10 0.9 0.1 90-100
0.006 10 0.96 0.06 100-110
0.004 10 1 0.04 110-120
1



66.41 = 10·(0.125/0.195)+60 = 10·((0.5-0.125-0.18)/(0.25-0.125))+60 =mode



percentile


developing mean formula according to relative frequency

developing  percentile formula


accumulate relative frequency -accumulate relative frequency up to the percentile group
accumulate frequency - relative frequency of the percentile group
N - population size
L - the lower limit of the percentile group
P% - population size in percentage

percentile calculation 20%


percentile group group width accumulate relative frequency relative frequency weight
%P c accumulate relative frequency relative frequency X
10 0.125 0.125 40-50
=> 10 0.25 0.125 50-60
10 0.5 0.25 60-70
10 0.68 0.18 70-80
10 0.8 0.12 80-90
10 0.9 0.1 90-100
10 0.96 0.06 100-110
10 1 0.04 110-120
1



56 =  10 · ( 0.125 / ( 0.2 - 0.125 ) ) + 50 =X0.2








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