Calculating the Mean - SSAT Upper Level: Quantitative
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What is the mean of the frequency set: $1$ occurs $2$ times, $3$ occurs $1$ time, $5$ occurs $1$ time?
What is the mean of the frequency set: $1$ occurs $2$ times, $3$ occurs $1$ time, $5$ occurs $1$ time?
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$\frac{5}{2}$. Weighted sum is $(1 \times 2) + (3 \times 1) + (5 \times 1) = 10$; divide by total frequency $4$.
$\frac{5}{2}$. Weighted sum is $(1 \times 2) + (3 \times 1) + (5 \times 1) = 10$; divide by total frequency $4$.
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What is the mean of the data set $\frac{1}{2}, \frac{3}{2}, \frac{5}{2}$?
What is the mean of the data set $\frac{1}{2}, \frac{3}{2}, \frac{5}{2}$?
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$\frac{3}{2}$. Sum the values $\frac{1}{2}+\frac{3}{2}+\frac{5}{2}=\frac{9}{2}$ and divide by $3$ to compute the average.
$\frac{3}{2}$. Sum the values $\frac{1}{2}+\frac{3}{2}+\frac{5}{2}=\frac{9}{2}$ and divide by $3$ to compute the average.
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What is the mean of the data set $0.2, 0.3, 0.5$?
What is the mean of the data set $0.2, 0.3, 0.5$?
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$\frac{1}{3}$. Sum the values $0.2+0.3+0.5=1.0$ and divide by $3$ to find the average.
$\frac{1}{3}$. Sum the values $0.2+0.3+0.5=1.0$ and divide by $3$ to find the average.
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Identify the mean of the arithmetic sequence $5, 7, 9, 11$.
Identify the mean of the arithmetic sequence $5, 7, 9, 11$.
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$8$. For an arithmetic sequence, the mean is the average of the first and last terms: $(5+11)/2$.
$8$. For an arithmetic sequence, the mean is the average of the first and last terms: $(5+11)/2$.
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If you add $k$ to every value in a data set, how does the mean change?
If you add $k$ to every value in a data set, how does the mean change?
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The mean increases by $k$. Adding $k$ to each value increases the total sum by $k$ times the number of values, thus raising the mean by $k$.
The mean increases by $k$. Adding $k$ to each value increases the total sum by $k$ times the number of values, thus raising the mean by $k$.
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What is the mean of the data set $-5, -1, 2, 4$?
What is the mean of the data set $-5, -1, 2, 4$?
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$0$. Sum the values $-5-1+2+4=0$ and divide by $4$ to find the average.
$0$. Sum the values $-5-1+2+4=0$ and divide by $4$ to find the average.
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State the mean of equally spaced numbers from $a$ to $b$ (inclusive).
State the mean of equally spaced numbers from $a$ to $b$ (inclusive).
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$\frac{a+b}{2}$. For an arithmetic sequence from $a$ to $b$, the mean is the midpoint between the first and last terms.
$\frac{a+b}{2}$. For an arithmetic sequence from $a$ to $b$, the mean is the midpoint between the first and last terms.
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A set has mean $10$ for $5$ numbers. A new number $15$ is added. What is the new mean?
A set has mean $10$ for $5$ numbers. A new number $15$ is added. What is the new mean?
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$\frac{65}{6}$. Original sum is $10 \times 5 = 50$; add $15$ for new sum $65$, then divide by $6$.
$\frac{65}{6}$. Original sum is $10 \times 5 = 50$; add $15$ for new sum $65$, then divide by $6$.
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A data set has sum $30$ and $6$ values. What is its mean?
A data set has sum $30$ and $6$ values. What is its mean?
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$5$. Divide the total sum $30$ by the number of values $6$ to compute the average.
$5$. Divide the total sum $30$ by the number of values $6$ to compute the average.
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If every value in a data set is multiplied by $c$, how does the mean change?
If every value in a data set is multiplied by $c$, how does the mean change?
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The mean is multiplied by $c$. Multiplying each value by $c$ scales the total sum by $c$, so the mean also scales by $c$.
The mean is multiplied by $c$. Multiplying each value by $c$ scales the total sum by $c$, so the mean also scales by $c$.
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Find the mean of $6$ numbers whose sum is $54$.
Find the mean of $6$ numbers whose sum is $54$.
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$9$. Divide the total sum $54$ by the number of values $6$ to find the average.
$9$. Divide the total sum $54$ by the number of values $6$ to find the average.
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A data set has mean $8$ with $4$ values. What is the sum of the values?
A data set has mean $8$ with $4$ values. What is the sum of the values?
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$32$. Multiply the mean $8$ by the number of values $4$ to find the total sum.
$32$. Multiply the mean $8$ by the number of values $4$ to find the total sum.
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Find the sum of $5$ numbers if their mean is $12$.
Find the sum of $5$ numbers if their mean is $12$.
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$60$. Multiply the mean $12$ by the number of values $5$ to compute the total sum.
$60$. Multiply the mean $12$ by the number of values $5$ to compute the total sum.
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A set has mean $8$ for $4$ numbers. One value $2$ is removed. What is the new mean?
A set has mean $8$ for $4$ numbers. One value $2$ is removed. What is the new mean?
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$10$. Original sum is $8 \times 4 = 32$; subtract $2$ for new sum $30$, then divide by $3$.
$10$. Original sum is $8 \times 4 = 32$; subtract $2$ for new sum $30$, then divide by $3$.
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Two groups have means $6$ (size $2$) and $9$ (size $4$). What is the combined mean?
Two groups have means $6$ (size $2$) and $9$ (size $4$). What is the combined mean?
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$8$. Total sum is $(6 \times 2) + (9 \times 4) = 48$; divide by total size $6$ to find combined mean.
$8$. Total sum is $(6 \times 2) + (9 \times 4) = 48$; divide by total size $6$ to find combined mean.
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What is the mean of the data set $1, 1, 2, 2, 2$?
What is the mean of the data set $1, 1, 2, 2, 2$?
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$\frac{8}{5}$. Sum the values $1+1+2+2+2=8$ and divide by $5$ to find the average.
$\frac{8}{5}$. Sum the values $1+1+2+2+2=8$ and divide by $5$ to find the average.
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What is the mean of the data set $4, 5, 5, 6$?
What is the mean of the data set $4, 5, 5, 6$?
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$5$. Sum the values $4+5+5+6=20$ and divide by $4$ to compute the average.
$5$. Sum the values $4+5+5+6=20$ and divide by $4$ to compute the average.
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What is the mean of the data set $10, 12, 14$?
What is the mean of the data set $10, 12, 14$?
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$12$. Sum the values $10+12+14=36$ and divide by $3$ to compute the average.
$12$. Sum the values $10+12+14=36$ and divide by $3$ to compute the average.
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What is the mean of the data set $-2, 0, 4$?
What is the mean of the data set $-2, 0, 4$?
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$\frac{2}{3}$. Sum the values $-2+0+4=2$ and divide by $3$ to find the average.
$\frac{2}{3}$. Sum the values $-2+0+4=2$ and divide by $3$ to find the average.
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What is the mean of the data set $1, 2, 2, 5$?
What is the mean of the data set $1, 2, 2, 5$?
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$\frac{5}{2}$. Sum the values $1+2+2+5=10$ and divide by $4$ to compute the average.
$\frac{5}{2}$. Sum the values $1+2+2+5=10$ and divide by $4$ to compute the average.
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What is the mean of the data set $3, 3, 3, 3, 3$?
What is the mean of the data set $3, 3, 3, 3, 3$?
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$3$. All values are identical, so the mean equals any value in the set.
$3$. All values are identical, so the mean equals any value in the set.
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What is the mean of the data set $2, 4, 6, 8$?
What is the mean of the data set $2, 4, 6, 8$?
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$5$. Sum the values $2+4+6+8=20$ and divide by $4$ to find the average.
$5$. Sum the values $2+4+6+8=20$ and divide by $4$ to find the average.
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State the formula for the mean of $n$ numbers $x_1, x_2, \dots, x_n$.
State the formula for the mean of $n$ numbers $x_1, x_2, \dots, x_n$.
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$\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}$. The mean is the sum of all values divided by the number of values.
$\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}$. The mean is the sum of all values divided by the number of values.
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What is the mean of the data set $0, 5, 10, 15$?
What is the mean of the data set $0, 5, 10, 15$?
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$\frac{15}{2}$. Sum the values $0+5+10+15=30$ and divide by $4$ to compute the average.
$\frac{15}{2}$. Sum the values $0+5+10+15=30$ and divide by $4$ to compute the average.
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What is the mean of the data set $7, 9$?
What is the mean of the data set $7, 9$?
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$8$. Sum the values $7+9=16$ and divide by $2$ to find the average.
$8$. Sum the values $7+9=16$ and divide by $2$ to find the average.
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