mean < median < mode
(Q2 – Q1) > (Q3 – Q2)
Longer left hand whisker
mode < median < mean
(Q2 – Q1) < (Q3 – Q2)
Longer right hand whisker
mode = median = mean
(Q2 – Q1) = (Q3 – Q2)
Interpolation to find a median Value =
Lower Class Boundary + (Cumulative Frequency X whatever you want to find, e.g. 0.25 for Q1, Minus the Cumulative Frequency before the modal class, Divide by Frequency in the modal class) Then Times by the Class Width.
The mean is very simple to calculate, If you are given a table with single integers on the top, e.g. 1,2,3,4(x) , and they have frequencys to them, e.g. the number 1 has a frequency of 5 (f). all you do is make a new table and calculate all the X's multiplied by the Frequencys, this is FX, then Add them together to get the sum of FX, Efx. Then devide Efx by the sum of all the Frequencys, EF, which is also the same as CF.
However if the Data is in groups, e.g. 0-9. Then Instead of Summing Efx, You should Sum the Frequency multiplied by the Midpoints of the Grouped data. e.g. mp of 0-9 is 4.5. So its Ef(mp) over Ef in grouped data.
Variance and Standard Deviation.
Variance = Sum of X^2 / n (The number of data sets, not the total) - Xbar^2(the mean squared) or see below for when it involves frequency's
Variance = Sum of FX^2 over the Sum of F, - Xbar^2(The mean squared).
The Standard Deviation is simply the Square Root of the Variance.
P(Event A or Event B) = P(AuB)
P(Both Events A and B) = P(AnB) (Remember this one because it had N in the middle like AND)
P(Not Event A) = …