Flashcards
Edexcel Statistics 1 - Key Facts
Cards in this deck (46)
- 1What 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. \[P(A\cap B)=0\]
- 2What 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). \[P(A\cap B)=P(A) \times P(B)\]
- 3\[P(A|B)=?\] (there is a rearranged version of this given in the formulae book)\[P(A|B)=\frac{P(A\cap B)}{P(B)}\]
- 4If events A and B are independent, then \(P(A|B)=?\)\[P(A|B)=P(A)\]
- 5If events A and B are independent, then \(P(B|A)=?\)\[P(B|A)=P(B)\]
- 6The addition law for events A and B is \[P(A\cup B)=?\] (given in formulae book)\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]
- 7\[P(A')=?\]\[P(A')=1-P(A)\] \(A'\) is called the complement of \(A\) and \(P(A')\) is the probability of \(A\) not happening
- 8For events A and B that are NOT independent, \[P(A\cap B)=?\]\[\begin{align*}
P(A\cap B)&=P(A)\times P(B|A)\\
& =P(B)\times P(A|B)
\end{align*}\] - 9Describe this shaded area using set notation\[A\cap B'\] or \[B'\cap A\]
- 10What is a sample space?The set of all the possible outcomes of a random experiment
- 11For any discrete random variable \(X\),\[\text{E}(aX + b) = ?\]\[\text{E}(aX + b) = a\text{E}(X) + b\]
- 12For any discrete random variable \(X\),\[\text{Var}(aX + b) = ?\]\[\text{Var}(aX + b) = a^2 \text{Var}(X)\]
- 13For a discrete random variable \(X\) taking values \(x_i\) with probabilities \(p_i\), \[\text{E}(X)=?\] (given in formulae book)\[\text{E}(X)=\sum x_i p_i \]
- 14For a discrete random variable \(X\) taking values \(x_i\) with probabilities \(p_i\), \[\text{Var}(X)=?\] (given in formulae book)\[\begin{align*}
\text{Var}(X)&=\sum x_i^2 p_i -\mu^2\\
&=\text{E}(X^2)-(\text{E}(X))^2
\end{align*}\] - 15Describe this shaded area using set notation\[A'\cap B\] or \[B\cap A'\]
- 16Describe this shaded area using set notation\[A \cup B\] or \[B \cup A\]
- 17Describe this shaded area using set notation\[A \cap B\]
- 18Describe this shaded area using set notation in two ways\[A'\cap B'\] or \[(A\cup B)'\]
- 19How is variance related to standard deviation?\[\text{variance}=(\text{stand. dev.})^2\] OR \[\text{stand. dev.}=\sqrt{\text{Variance}}\]
- 20The cumulative distribution function for a discrete random variable: \[F(x_0)=P(?)\]\[F(x_0)=P(X\leq x_0)\]
- 21If \(X\) has a normal distribution with mean \(\mu\) and standard deviation \(\sigma^2\), how do you transform it to the \(Z\) distribution?\[Z=\frac{X-\mu}{\sigma}\]
- 22\[\text{Interquartile range (IQR)}=?\]\[\text{IQR}=Q_3-Q_1\] where \(Q_3\) is the upper quartile and \(Q_1\) the lower quartile
- 23What is the formula for the mean of a set of data?\[\bar{x} =\frac{\sum x}{n} \text{ or }\frac{\sum fx}{\sum f}\]
- 24What is the underlying feature associated with each of the bars in a histogram?Area is proportional to frequency
- 25How do you find the range of a set of data?\[\text{range}=\text{highest value}-\text{lowest value}\]
- 26What is the formula for the standard deviation of a set of data?\[\sigma =\sqrt{\frac{\sum x^2}{n}-(\bar{x})^2}\] OR \[\sigma =\sqrt{\frac{\sum fx^2}{\sum f}-(\bar{x})^2}\]
- 27What is a continuous variable?A variable that can take any value in a given range
- 28What is a discrete variable?A variable that can take only specific values in a given range
- 29What is \(r\) (the product moment correlation coefficient) a measure of?\(r\) is a measure of linear correlation
- 30\(r\) is the product moment correlation coefficient \[\begin{align*} r=1 &\Rightarrow ?\\ r=-1 &\Rightarrow ?\\ r=0 &\Rightarrow ?\\ \end{align*}\]\[\begin{align*}
r=1 &\Rightarrow \text{perfect +ve linear correlation}\\
r=-1 &\Rightarrow \text{perfect -ve linear correlation}\\
r=0 &\Rightarrow \text{no linear correlation}\\
\end{align*}\] - 31On a histogram, \(\text{frequency density}=?\)\[\text{f.d.}=\frac{\text{frequency}}{\text{class width}}\]
- 32If \(Q_2-Q_1Positive skew
- 33If \(Q_2-Q_1>Q_3-Q_2\), what type of skew does the data have?Negative skew
- 34If \(Q_2-Q_1=Q_3-Q_2\), what type of distribution do we have?A symmetrical distribution
- 35If \(\text{mode}<\text{mean}<\text{median}\), what type of skew do we have? (This is true even if we only know 2 of mean, mode and median)Positive skew
- 36If \(\text{mode}=\text{mean}=\text{median}\), what type of distribution do we have? (This is true even if we only know 2 of mean, mode and median)A symmetrical distribution
- 37If \(\text{mode}>\text{mean}>\text{median}\), what type of skew do we have? (This is true even if we only know 2 of mean, mode and median)Negative skew
- 38How 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.
- 39Which measures of location and dispersion are affected by extreme values?Mean, standard deviation and range
- 40Which measures of location and dispersion are NOT affected by extreme values?Median and IQR
- 41When comparing data sets, what 3 measures could you use in your comparison?1. A measure of location
2. A measure of dispersion
3. Skewness - 42What is meant by an independent (or explanatory) variable?A variable that is set independently of the other variable.
- 43What 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 - 44Is the product moment correlation coefficient affected by coded data?No.
\(r\) is not affected by coding. - 45For a discrete uniform distribution \(X\) defined over the values \(1, 2, 3, ..., n\), \[\text{E}(X)=?\]\[E(X)=\frac{n+1}{2}\]
- 46For 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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- Key facts and formulae which must be known for the Edexcel Statistics 1 examination.
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- Daniel Cox
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- Created by Daniel Cox · Jun 2, 2016
- Copied by Daniel Cox · Jun 13, 2016
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