No. of doors in a house.
4 |4 |4 |4 |5 |5 |5 |5 |5 |6 | |6 |7 |7 |7 |8 |8 |8 |8 |8 |9 | |9 |9 |9 |9 |10 |10 |10 |10 |10 |11 | |11 |11 |11 |11 |12 |13 |13 |14 |14 |15 | |15 |16 |16 |17 |18 |19 |19 |19 |20 |20 | |
K = 1 + 3.322 Log N
K = 1 + 3.322 Log 50
K = 7.34 ≈ 7
R = 20 ' 4
R = 16
Class width:
i = R / K
i = 16 / 7
i = 2.2857 ≈ 2
Class Limit |Frequency |Class Mark |Class Boundaries |CF < |CF > |RF
% |Fi Xi |F ( x ' mean)2 | |4 ' 5 |2 |4.5 |5.5 |2 |24 |8.3% |9 |87.12 | |5 ' 6 |2 |5.5 |6.5 |4 |22 |8.3% |11 |62.72 | |6 ' 8 |3 |7 |8.5 |7 |20 |12.5% |21 |50.43 | |8 ' 9 |2 |8.5 |9.5 |9 |17 |8.3% |17 |13.52 | |9 ' 10 |2 |9.5 |10.5 |11 |15 |8.3% |19 |5.12 | |10 ' 11 |2 |10.5 |11.5 |13 |13 |8.3% |21 |.72 | |11 ' 12 |2 |11.5 |12.5 |15 |11 |8.3% |23 |.32 | |13 ' 14 |3 |13.5 |14.5 |18 |9 |12.5% |40.5 |17.28 | |15 ' 18 |4 |16.5 |18.5 |22 |6 |16.6% |66 |116.64 | |19 ' 20 |2 |19.5 |20.5 |24 |2 |8.3% |39 |141.12 | |
RF% = 99.7% ≈ 100%
∑Fi Xi = 266.5
Mean = 266.5 / 24 = 11.10
Median = XLB + ( N/2 ' CFP ) i
Fm
Median Class: (13 ' 14)
N/2 = 24/2 = 12
XLB = 12.5
CFP = 15
Fm = 3
i = 2
12.5 + ( 12 ' 15 ) 2 = 10.5
3
• 50% of the observation are above 10.5.
Modal Class: (13 ' 14)
XLB = 12.5
A1 = 1
A2 = 1
12.5 + ( 1 ) 2 = 13.5
1+1
• Most of the observations are closer to 13.5.
Inter Quartile Range
IQR: Q3 ' Q1
IQR = 14.5 ' 6.8
IQR = 7.7
First Quartile Class: (6 ' 8)
1/4N = 1/4 (24) = 6
XLB = 5.5
CFP = 4
F = 3
i = 2
Q1 = 5.5 ( 6 ' 4 ) 2
3
Q1 = 6.8
Second Quartile Class: (10 ' 11)
2/4N = 2/4 (24) = 12
XLB = 9.5
CFP = 11
F = 2
i = 2
Q2 = 9.5 ( 12 ' 11 ) 2
2
Q2 = 10.5
Third Quartile Class: (13 ' 14)
3/4N = 3/4 (24) = 18
XLB = 12.5
CFP = 15
F = 3
i = 2
Q3 = 12.5 ( 18 ' 15 ) 2
3
Q3 = 14.5
Decile:
D7: (13 ' 14)
7/10N = 7/10 (24) = 16.8
XLB = 12.5
CFP = 15
F = 3
i = 2
D7 = 12.5...