Calculations From Data Displays - SSAT Middle Level Quantitative

1. What is the percent change from $80$ to $60$?

   $25\%$ decrease. Divides the negative difference by the original and multiplies by 100 for percent decrease.

2. What is the formula for percent change from an old value $o$ to a new value $n$?

   $\frac{n-o}{o}\times 100\%$. Calculates percent change by finding the difference relative to the old value and multiplying by 100.

3. What is the average rate per item if a display shows total $T$ across $n$ equal groups?

   $\frac{T}{n}$. Divides the total by the number of groups to compute the mean value per group.

4. What is the total number of students if $12$ students are $30\%$ of the class?

   $40$. Divides the part by its percentage in decimal form to find the total class size.

5. What is the total frequency if a table shows counts $7$, $9$, $4$, and $10$?

   $30$. Adds up all individual category counts to obtain the overall frequency total.

6. What is the value after a $r\%$ decrease from an original amount $A$?

   $A\left(1-\frac{r}{100}\right)$. Subtracts the percentage decrease from the original by multiplying by $(1 - r/100)$.

7. What percent of the total is $15$ out of $60$?

   $25\%$. Divides 15 by 60 and multiplies by 100 to express the proportion as a percentage.

8. What is the combined percent if two categories are $35\%$ and $15\%$ of a display?

   $50\%$. Adds the two percentages together to find their total combined share of the display.

9. What is the new value after a $20\%$ increase from $50$?

   $60$. Multiplies 50 by 1.20 to apply a 20 percent increase to the original amount.

10. What is the percent change from $40$ to $50$?

    $25\%$ increase. Divides the difference by the original and multiplies by 100 to find the percent increase.

11. What is the new value after a $15\%$ decrease from $200$?

    $170$. Multiplies 200 by 0.85 to apply a 15 percent decrease to the original value.

12. What is the difference between $68$ and $52$?

    $16$. Subtracts the smaller value from the larger to find the absolute difference.

13. What is the remaining percent if one category is $62\%$ of the total?

    $38\%$. Subtracts the given percentage from 100 percent to find the remaining portion.

14. What is the whole $w$ if you know the part $p$ and percent $r\%$?

    $w=\frac{p}{r/100}$. Divides the part by the decimal percent to determine the total whole amount.

15. What is the formula for the difference between two values $a$ and $b$ (how far apart)?

    $|a-b|$. Uses absolute value to ensure the difference represents the positive distance between two points.

16. What is the percent formula for a part $p$ out of a whole $w$?

    $\text{percent}=\frac{p}{w}\times 100\%$. Divides the part by the whole and multiplies by 100 to express the ratio as a percentage.

17. What is the total if a bar chart shows $24$ for Group A and Group B is $8$ more than A?

    $56$. Adds Group A's value to Group B's value, which is 24 plus 8, to get the total.

18. What percent of $50$ is $20$?

    $40\%$. Divides 20 by 50 and multiplies by 100 to convert the ratio to a percentage.

19. What is the percent of a category with frequency $f$ out of total $T$?

    $\frac{f}{T}\times 100\%$. Divides the category frequency by the total and multiplies by 100 to find its percentage share.

20. What is $25\%$ of $80$?

    $20$. Multiplies 80 by 0.25 to determine 25 percent of the specified value.

21. What is the total of the frequencies in a data display used to represent?

    The total number of data points (the sample size). Summing frequencies in a data display gives the overall count of observations or sample size.

22. What is the part $p$ if you know the whole $w$ and percent $r\%$?

    $p=\frac{r}{100}\,w$. Multiplies the whole by the decimal equivalent of the percent to find the corresponding part.

23. What is the value after a $r\%$ increase from an original amount $A$?

    $A\left(1+\frac{r}{100}\right)$. Adds the percentage increase to the original by multiplying by $(1 + r/100)$.

24. What fraction of the total is $18$ out of $72$, in simplest form?

    $\frac{1}{4}$. Simplifies the ratio 18/72 by dividing numerator and denominator by 18.

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