ISEE Middle Level Quantitative Reasoning Flashcards: Calculating Averages

What this deck covers

This deck focuses on Calculating Averages, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Quantitative Reasoning.

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

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

Flashcard 2: What is the mean of the data set $4, 6, 10$?

Answer: $\frac{20}{3}$. Sum the values $4+6+10=20$ and divide by $3$ to find the average.

Flashcard 3: What is the mean of the data set $7, 7, 7, 7, 7$?

Answer: $7$. When all data points are identical, the mean equals that common value.

Flashcard 4: What is the mean of the data set $2, 3, 5, 10$?

Answer: $5$. Sum the values $2+3+5+10=20$ and divide by $4$ to compute the average.

Flashcard 5: What is the mean of the data set $1, 2, 3, 4, 10$?

Answer: $4$. Sum the values $1+2+3+4+10=20$ and divide by $5$ for the mean.

Flashcard 6: What is the mean of the data set $12, 15, 18$?

Answer: $15$. Sum the values $12+15+18=45$ and divide by $3$ to obtain the mean.

Flashcard 7: 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 find the average.

Flashcard 8: What is the mean of the data set $-2, 0, 6$?

Answer: $\frac{4}{3}$. Sum the values $-2+0+6=4$ and divide by $3$ to calculate the mean.

Flashcard 9: What is the mean of the data set $-3, -1, 2, 6$?

Answer: $1$. Sum the values $-3+(-1)+2+6=4$ and divide by $4$ for the average.

Flashcard 10: Identify the mean of the data set $\frac{1}{2}, \frac{1}{2}, \frac{3}{2}$.

Answer: $\frac{5}{6}$. Sum the fractions $\frac{1}{2}+\frac{1}{2}+\frac{3}{2}=\frac{5}{2}$ and divide by $3$.

Flashcard 11: What is the mean of the data set $0.2, 0.3, 0.5$?

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

Flashcard 12: State the formula for a weighted mean with values $x_i$ and weights $w_i$.

Answer: $\text{weighted mean}=\frac{\sum w_i x_i}{\sum w_i}$. The weighted mean is the sum of each value multiplied by its weight, divided by the total weight.

Flashcard 13: What is the weighted mean of $80$ (weight $2$) and $90$ (weight $3$)?

Answer: $86$. Compute $(80 \times 2 + 90 \times 3)/(2+3)$ to account for the weights.

Flashcard 14: What is the weighted mean of scores $70, 80, 90$ with weights $1, 2, 1$?

Answer: $80$. Calculate $(70 \times 1 + 80 \times 2 + 90 \times 1)/(1+2+1)$ using the given weights.

Flashcard 15: What is the mean if the sum of $8$ numbers is $60$?

Answer: $\frac{15}{2}$. Divide the total sum $60$ by the number of values $8$ to find the average.

Flashcard 16: What is the sum of a data set with mean $12$ and $5$ values?

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

Flashcard 17: A set has mean $10$ for $6$ numbers. What is the new mean after adding $16$?

Answer: $\frac{76}{7}$. Original sum is $10 \times 6 = 60$; add $16$ for new sum $76$, divide by $7$.

Flashcard 18: A set has mean $8$ for $5$ numbers. What is the new mean after removing a value of $3$?

Answer: $\frac{37}{4}$. Original sum is $8 \times 5 = 40$; subtract $3$ for new sum $37$, divide by $4$.

Flashcard 19: A set has mean $9$ for $4$ numbers. What value must be added to make the new mean $10$?

Answer: $14$. Original sum is $9 \times 4 = 36$; for new mean $10$ with $5$ numbers, new sum is $50$, so add $14$.

Flashcard 20: The mean of $5$ numbers is $6$. Four numbers are $4, 5, 7, 8$. What is the fifth number?

Answer: $6$. Total sum is $6 \times 5 = 30$; subtract sum of known numbers $4+5+7+8=24$ to find the fifth.

Flashcard 21: What is the mean of consecutive integers $5, 6, 7, 8, 9$?

Answer: $7$. Sum the integers $5+6+7+8+9=35$ and divide by $5$ for the mean.

Flashcard 22: What is the mean of the consecutive integers from $1$ to $9$ inclusive?

Answer: $5$. The mean of consecutive integers from $1$ to $9$ is the middle value, which is $5$.

Flashcard 23: State the mean of two numbers $a$ and $b$ using a formula.

Answer: $\frac{a+b}{2}$. The mean of two numbers is their sum divided by $2$.

Flashcard 24: Find and correct the mean: For $2, 4, 6, 8$, a student wrote $\frac{2+4+6+8}{3}=7$.

Answer: $\frac{2+4+6+8}{4}=5$. The student divided by $3$ instead of $4$; correct by using the proper count of values.