Revise: Statistics
Measuring spread with range, IQR, variance and standard deviation; cumulative frequency tables and the ogive; and scatter diagrams and the correlation coefficient.
Range = maxβmin. IQR = QββQβ (robust to outliers).
4..30 dataset β range=26, IQR=15.
Running total, plotted at UPPER class boundary.
Boundaries 10-50 β cumulative 5,18,35,45,50.
r β [β1,1]. Sign=direction, |r|=strength.
r=β0.85 β strong negative correlation.
Qβ=median of lower half; Qβ=median of upper half.
12,5,19,8,23,3 β range=20.
Square deviations first β raw deviations always sum to 0.
1,3,5,7,9 β variance=8.
Joining cumulative points gives an S-shaped ogive.
0-5(3),5-10(7) β cumulative at 10 is 10.
Median: read at n/2. Qβ: n/4. Qβ: 3n/4.
n=50 β median at cumulative freq 25 β x=24.1.
Upward trend = positive; downward = negative; no pattern = none.
Car age up, resale value down β negative correlation.
Numerator sign shows direction; whole ratio bounded to [β1,1].
|β0.95| is stronger than |0.4|.