Calculating the Mean - SSAT Upper Level Quantitative

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

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

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

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

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

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

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

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

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

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

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

   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 $k$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Study these flashcards