Statistics & Probability - ACT Math
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What is the median of a data set?
What is the median of a data set?
The middle value when data is arranged in order. For an even number of values, the median is the mean of the two middle values.
The middle value when data is arranged in order. For an even number of values, the median is the mean of the two middle values.
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A bag has $5$ red and $3$ blue marbles. If a red marble is drawn and not replaced, what is the probability the next marble is also red?
A bag has $5$ red and $3$ blue marbles. If a red marble is drawn and not replaced, what is the probability the next marble is also red?
$\dfrac{4}{7}$ (4 red marbles left out of 7 total remaining)
$\dfrac{4}{7}$ (4 red marbles left out of 7 total remaining)
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Find the median of: $3, 7, 9, 12$
Find the median of: $3, 7, 9, 12$
$8$ (average of middle two: $\dfrac{7+9}{2} = 8$)
$8$ (average of middle two: $\dfrac{7+9}{2} = 8$)
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What is the probability of flipping heads on a fair coin?
What is the probability of flipping heads on a fair coin?
$\dfrac{1}{2}$ or $0.5$ or $50%$
$\dfrac{1}{2}$ or $0.5$ or $50%$
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What is the multiplication principle (counting principle)?
What is the multiplication principle (counting principle)?
If one event can occur in $m$ ways and another in $n$ ways, together they can occur in $m \times n$ ways
If one event can occur in $m$ ways and another in $n$ ways, together they can occur in $m \times n$ ways
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A spinner has $8$ equal sections numbered $1$ to $8$. What is the probability of landing on an even number?
A spinner has $8$ equal sections numbered $1$ to $8$. What is the probability of landing on an even number?
$\dfrac{1}{2}$ (4 even numbers: $2, 4, 6, 8$ out of 8 total)
$\dfrac{1}{2}$ (4 even numbers: $2, 4, 6, 8$ out of 8 total)
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What does it mean for two events to be independent?
What does it mean for two events to be independent?
Events $A$ and $B$ are independent if $P(A|B) = P(A)$ (equivalently $P(A \cap B) = P(A)P(B)$).
Events $A$ and $B$ are independent if $P(A|B) = P(A)$ (equivalently $P(A \cap B) = P(A)P(B)$).
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Find the mean of: $3, 5, 7, 9, 11$
Find the mean of: $3, 5, 7, 9, 11$
$7$ ($\dfrac{3+5+7+9+11}{5} = \dfrac{35}{5} = 7$)
$7$ ($\dfrac{3+5+7+9+11}{5} = \dfrac{35}{5} = 7$)
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What is the mode of: $1, 2, 3, 4, 5$?
What is the mode of: $1, 2, 3, 4, 5$?
No mode (all values appear equally often)
No mode (all values appear equally often)
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In how many ways can $5$ books be arranged on a shelf?
In how many ways can $5$ books be arranged on a shelf?
$120$ ($5! = 120$)
$120$ ($5! = 120$)
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A class has test scores: $70, 75, 80, 85, 90$. What is the median?
A class has test scores: $70, 75, 80, 85, 90$. What is the median?
$80$ (middle value)
$80$ (middle value)
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What is a permutation?
What is a permutation?
An arrangement where order matters; $P(n,r) = \dfrac{n!}{(n-r)!}$
An arrangement where order matters; $P(n,r) = \dfrac{n!}{(n-r)!}$
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Find the range of: $5, 12, 3, 18, 7$
Find the range of: $5, 12, 3, 18, 7$
$15$ ($18 - 3 = 15$)
$15$ ($18 - 3 = 15$)
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What is expected value?
What is expected value?
The average outcome if an experiment is repeated many times; $E(X) = \sum x_i \cdot P(x_i)$ (expected net gain if costs are subtracted)
The average outcome if an experiment is repeated many times; $E(X) = \sum x_i \cdot P(x_i)$ (expected net gain if costs are subtracted)
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How many different $4$-letter "words" can be formed from the letters in MATH if no letter is repeated?
How many different $4$-letter "words" can be formed from the letters in MATH if no letter is repeated?
$24$ ($4! = 4 \times 3 \times 2 \times 1 = 24$)
$24$ ($4! = 4 \times 3 \times 2 \times 1 = 24$)
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A card is drawn from a standard deck. What is the probability of NOT drawing a heart?
A card is drawn from a standard deck. What is the probability of NOT drawing a heart?
$\dfrac{3}{4}$ or $0.75$ ($1 - \dfrac{13}{52} = \dfrac{39}{52} = \dfrac{3}{4}$)
$\dfrac{3}{4}$ or $0.75$ ($1 - \dfrac{13}{52} = \dfrac{39}{52} = \dfrac{3}{4}$)
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Data set: $5, 10, 15, 20, 25$. If each value is multiplied by $2$, what happens to the mean?
Data set: $5, 10, 15, 20, 25$. If each value is multiplied by $2$, what happens to the mean?
The mean is also multiplied by $2$ (new mean $= 30$)
The mean is also multiplied by $2$ (new mean $= 30$)
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What is conditional probability $P(A|B)$?
What is conditional probability $P(A|B)$?
The probability of $A$ occurring given that $B$ has already occurred: $P(A|B) = \dfrac{P(A \text{ and } B)}{P(B)}$
The probability of $A$ occurring given that $B$ has already occurred: $P(A|B) = \dfrac{P(A \text{ and } B)}{P(B)}$
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A jar contains $4$ red, $6$ green, and $10$ yellow marbles. What is the probability of selecting a green marble?
A jar contains $4$ red, $6$ green, and $10$ yellow marbles. What is the probability of selecting a green marble?
$\dfrac{6}{20} = \dfrac{3}{10}$ (6 green out of 20 total)
$\dfrac{6}{20} = \dfrac{3}{10}$ (6 green out of 20 total)
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What is the mean (average) of a data set?
What is the mean (average) of a data set?
The sum of all values divided by the number of values: $\text{mean} = \dfrac{\sum x_i}{n}$
The sum of all values divided by the number of values: $\text{mean} = \dfrac{\sum x_i}{n}$
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