Test1 Practicing

mean is متوسط الحسابي
median is الوسيط divided by its count (by 2 if it’s two numbers)
mode is المنوال
range is المدى
Trimmed mean: after sorting the data remove 25% from left and 25% from the right then do المتوسط الحسابي for the remaining data
Variance: $s^2=\frac{\sum x_i^2-\frac{(\sum x_i{)}^2}{n}}{n-1}$
where ( x i ) represents each data point
Deviance is the square root of Variance

A ∩ B the probability of A and B occurring together at the same time
Formula: P(A∩B)=P(A∣B)⋅P(B)
A ∣ B is A occurring given that B has occurred (| is given)
$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$
Venn Diagram is the overlapping circles thingy
P(A ∩ B′)=P(A)−P(A ∩ B) (which excludes B)
P(A′ ∩ B′)=1−P(A ∪ B)
P(A ∪ B) either event A occurs, or event B occurs, or both occur.
The union includes all outcomes that belong to at least one of the events.
P(A ∪ B)=P(A) + P(B) − P(A ∩ B)
^^ why do we subtract (A ∩ B)? to get rid of the duplicate values from A and B overlapping
$P(B^{\prime }\mid A)=\frac{P(A\cap B^{\prime })}{P(A)}$
Checking for Independence:
If P(A∣B)=P(A)P(A∣B)=P(A), then A and B are independent.
$P(A^{\prime }\cup B)=P(A^{\prime })+P(B)-P(A^{\prime }\cap B)$
P(random)= total data / the data part given
key: either or is mentioned: most likely a union