Edexcel Statistics 1 - Key Facts

Question	Answer
What does it mean if events A and B are mutually exclusive? Also, $P(A\cap B)=?$	Events A and B cannot happen at the same time. $P(A\cap B)=0$
What does it mean if events A and B are independent? Also, $P(A\cap B)=?$	If A happens, this does not affect the probability of B happening (and vice versa). $P(A\cap B)=P(A) \times P(B)$
$P(A\|B)=?$ (there is a rearranged version of this given in the formulae book)	$P(A\|B)=\frac{P(A\cap B)}{P(B)}$
If events A and B are independent, then $P(A\|B)=?$	$P(A\|B)=P(A)$
If events A and B are independent, then $P(B\|A)=?$	$P(B\|A)=P(B)$
The addition law for events A and B is $P(A\cup B)=?$ (given in formulae book)	$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$P(A')=?$	$P(A')=1-P(A)$ $A'$ is called the complement of $A$ and $P(A')$ is the probability of $A$ not happening
For events A and B that are NOT independent, $P(A\cap B)=?$	$\begin{align} P(A\cap B)&=P(A)\times P(B\|A)\\ & =P(B)\times P(A\|B) \end{align}$
Describe this shaded area using set notation Image: 7fe24a27-4d4c-4394-b761-66a7ff1b140d.PNG (image/PNG)	$A\cap B'$ or $B'\cap A$
What is a sample space?	The set of all the possible outcomes of a random experiment
For any discrete random variable $X$ , $\text{E}(aX + b) = ?$	$\text{E}(aX + b) = a\text{E}(X) + b$
For any discrete random variable $X$ , $\text{Var}(aX + b) = ?$	$\text{Var}(aX + b) = a^2 \text{Var}(X)$
For a discrete random variable $X$ taking values $x_i$ with probabilities $p_i$ , $\text{E}(X)=?$ (given in formulae book)	$\text{E}(X)=\sum x_i p_i$
For a discrete random variable $X$ taking values $x_i$ with probabilities $p_i$ , $\text{Var}(X)=?$ (given in formulae book)	$\begin{align} \text{Var}(X)&=\sum x_i^2 p_i -\mu^2\\ &=\text{E}(X^2)-(\text{E}(X))^2 \end{align}$
Describe this shaded area using set notation Image: a0d16dcc-e38b-43b9-9776-72ea3c79b208.PNG (image/PNG)	$A'\cap B$ or $B\cap A'$
Describe this shaded area using set notation Image: 49d67efe-6a8e-4af0-b978-391f68f2f47a.PNG (image/PNG)	$A \cup B$ or $B \cup A$
Describe this shaded area using set notation Image: 3531ebf4-07ee-43b7-989a-585f9f5963a5.PNG (image/PNG)	$A \cap B$
Describe this shaded area using set notation in two ways Image: bb689cdf-3e5c-4a4a-9591-b36bba134e26.PNG (image/PNG)	$A'\cap B'$ or $(A\cup B)'$
How is variance related to standard deviation?	$\text{variance}=(\text{stand. dev.})^2$ OR $\text{stand. dev.}=\sqrt{\text{Variance}}$
The cumulative distribution function for a discrete random variable: $F(x_0)=P(?)$	$F(x_0)=P(X\leq x_0)$
If $X$ has a normal distribution with mean $\mu$ and standard deviation $\sigma^2$ , how do you transform it to the $Z$ distribution?	$Z=\frac{X-\mu}{\sigma}$
$\text{Interquartile range (IQR)}=?$	$\text{IQR}=Q_3-Q_1$ where $Q_3$ is the upper quartile and $Q_1$ the lower quartile
What is the formula for the mean of a set of data?	$\bar{x} =\frac{\sum x}{n} \text{ or }\frac{\sum fx}{\sum f}$
What is the underlying feature associated with each of the bars in a histogram?	Area is proportional to frequency
How do you find the range of a set of data?	$\text{range}=\text{highest value}-\text{lowest value}$
What is the formula for the standard deviation of a set of data?	$\sigma =\sqrt{\frac{\sum x^2}{n}-(\bar{x})^2}$ OR $\sigma =\sqrt{\frac{\sum fx^2}{\sum f}-(\bar{x})^2}$
What is a continuous variable?	A variable that can take any value in a given range
What is a discrete variable?	A variable that can take only specific values in a given range
What is $r$ (the product moment correlation coefficient) a measure of?	$r$ is a measure of linear correlation
$r$ is the product moment correlation coefficient $\begin{align} r=1 &\Rightarrow ?\\ r=-1 &\Rightarrow ?\\ r=0 &\Rightarrow ?\\ \end{align}$	$\begin{align} r=1 &\Rightarrow \text{perfect +ve linear correlation}\\ r=-1 &\Rightarrow \text{perfect -ve linear correlation}\\ r=0 &\Rightarrow \text{no linear correlation}\\ \end{align}$
On a histogram, $\text{frequency density}=?$	$\text{f.d.}=\frac{\text{frequency}}{\text{class width}}$
If $Q_2-Q_1<Q_3-Q_2$ , what type of skew does the data have?	Positive skew
If $Q_2-Q_1>Q_3-Q_2$ , what type of skew does the data have?	Negative skew
If $Q_2-Q_1=Q_3-Q_2$ , what type of distribution do we have?	A symmetrical distribution
If $\text{mode}<\text{mean}<\text{median}$ , what type of skew do we have? (This is true even if we only know 2 of mean, mode and median)	Positive skew
If $\text{mode}=\text{mean}=\text{median}$ , what type of distribution do we have? (This is true even if we only know 2 of mean, mode and median)	A symmetrical distribution
If $\text{mode}>\text{mean}>\text{median}$ , what type of skew do we have? (This is true even if we only know 2 of mean, mode and median)	Negative skew
How would you use the formula $\frac{3(\text{mean}-\text{median})}{\text{standard deviation}}$ to determine how skewed some data are?	The closer the number is to zero the more symmetrical the data. The larger the number the greater the skew. A positive number implies positive skew. A negative number implies negative skew.
Which measures of location and dispersion are affected by extreme values?	Mean, standard deviation and range
Which measures of location and dispersion are NOT affected by extreme values?	Median and IQR
When comparing data sets, what 3 measures could you use in your comparison?	1. A measure of location 2. A measure of dispersion 3. Skewness
What is meant by an independent (or explanatory) variable?	A variable that is set independently of the other variable.
What is meant by a dependent (or response) variable?	A variable whose values depend on the values of the independent variable. i.e. they are determined by the values of the independent variable
Is the product moment correlation coefficient affected by coded data?	No. $r$ is not affected by coding.
For a discrete uniform distribution $X$ defined over the values $1, 2, 3, ..., n$ , $\text{E}(X)=?$	$E(X)=\frac{n+1}{2}$
For a discrete uniform distribution $X$ defined over the values $1, 2, 3, ..., n$ , $\text{Var}(X)=?$	$\text{Var}(X)=\frac{n^2-1}{12}$

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Edexcel Statistics 1 - Key Facts

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