SSAT Upper Level Quantitative Flashcards: Calculating The Mean

What this deck covers

This deck focuses on Calculating The Mean, giving you a quick way to review the definitions, rules, and examples that matter most for SSAT Upper Level Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the mean of the data set $0.2, 0.3, 0.5$?

Answer: $\frac{1}{3}$. Sum the values $0.2+0.3+0.5=1.0$ and divide by $3$ to find the average.

Flashcard 2: Identify the mean of the arithmetic sequence $5, 7, 9, 11$.

Answer: $8$. For an arithmetic sequence, the mean is the average of the first and last terms: $(5+11)/2$.

Flashcard 3: What is the mean of the data set $2, 4, 6, 8$?

Answer: $5$. Sum the values $2+4+6+8=20$ and divide by $4$ to find the average.

Flashcard 4: State the mean of equally spaced numbers from $a$ to $b$ (inclusive).

Answer: $\frac{a+b}{2}$. For an arithmetic sequence from $a$ to $b$, the mean is the midpoint between the first and last terms.

Flashcard 5: A set has mean $10$ for $5$ numbers. A new number $15$ is added. What is the new mean?

Answer: $\frac{65}{6}$. Original sum is $10 \times 5 = 50$; add $15$ for new sum $65$, then divide by $6$.

Flashcard 6: If you add $k$ to every value in a data set, how does the mean change?

Answer: 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 $k$.

Flashcard 7: What is the mean of the data set $\frac{1}{2}, \frac{3}{2}, \frac{5}{2}$?

Answer: $\frac{3}{2}$. Sum the values $\frac{1}{2}+\frac{3}{2}+\frac{5}{2}=\frac{9}{2}$ and divide by $3$ to compute the average.

Flashcard 8: What is the mean of the frequency set: $1$ occurs $2$ times, $3$ occurs $1$ time, $5$ occurs $1$ time?

Answer: $\frac{5}{2}$. Weighted sum is $(1 \times 2) + (3 \times 1) + (5 \times 1) = 10$; divide by total frequency $4$.

Flashcard 9: What is the mean of the data set $3, 3, 3, 3, 3$?

Answer: $3$. All values are identical, so the mean equals any value in the set.

Flashcard 10: State the formula for the mean of $n$ numbers $x_1, x_2, \dots, x_n$.

Answer: $\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}$. The mean is the sum of all values divided by the number of values.

Flashcard 11: Two groups have means $6$ (size $2$) and $9$ (size $4$). What is the combined mean?

Answer: $8$. Total sum is $(6 \times 2) + (9 \times 4) = 48$; divide by total size $6$ to find combined mean.

Flashcard 12: What is the mean of the data set $10, 12, 14$?

Answer: $12$. Sum the values $10+12+14=36$ and divide by $3$ to compute the average.

Flashcard 13: What is the mean of the data set $1, 1, 2, 2, 2$?

Answer: $\frac{8}{5}$. Sum the values $1+1+2+2+2=8$ and divide by $5$ to find the average.

Flashcard 14: What is the mean of the data set $0, 5, 10, 15$?

Answer: $\frac{15}{2}$. Sum the values $0+5+10+15=30$ and divide by $4$ to compute the average.

Flashcard 15: What is the mean of the data set $7, 9$?

Answer: $8$. Sum the values $7+9=16$ and divide by $2$ to find the average.

Flashcard 16: What is the mean of the data set $1, 2, 2, 5$?

Answer: $\frac{5}{2}$. Sum the values $1+2+2+5=10$ and divide by $4$ to compute the average.

Flashcard 17: What is the mean of the data set $-2, 0, 4$?

Answer: $\frac{2}{3}$. Sum the values $-2+0+4=2$ and divide by $3$ to find the average.

Flashcard 18: A data set has sum $30$ and $6$ values. What is its mean?

Answer: $5$. Divide the total sum $30$ by the number of values $6$ to compute the average.

Flashcard 19: A set has mean $8$ for $4$ numbers. One value $2$ is removed. What is the new mean?

Answer: $10$. Original sum is $8 \times 4 = 32$; subtract $2$ for new sum $30$, then divide by $3$.

Flashcard 20: A data set has mean $8$ with $4$ values. What is the sum of the values?

Answer: $32$. Multiply the mean $8$ by the number of values $4$ to find the total sum.

Flashcard 21: Find the mean of $6$ numbers whose sum is $54$.

Answer: $9$. Divide the total sum $54$ by the number of values $6$ to find the average.

Flashcard 22: What is the mean of the data set $-5, -1, 2, 4$?

Answer: $0$. Sum the values $-5-1+2+4=0$ and divide by $4$ to find the average.

Flashcard 23: Find the sum of $5$ numbers if their mean is $12$.

Answer: $60$. Multiply the mean $12$ by the number of values $5$ to compute the total sum.

Flashcard 24: If every value in a data set is multiplied by $c$, how does the mean change?

Answer: The mean is multiplied by $c$. Multiplying each value by $c$ scales the total sum by $c$, so the mean also scales by $c$.

Flashcard 25: What is the mean of the data set $4, 5, 5, 6$?

Answer: $5$. Sum the values $4+5+5+6=20$ and divide by $4$ to compute the average.