QuestionDetermine the missing proportions and percentages for Verbal SAT score intervals given the frequencies:
$700-799$ : 17, $600-699$ : 22, $500-599$ : 15, $400-499$ : 4, $300-399$ : 2.

Studdy Solution

STEP 1

Assumptions1. The frequency (f) represents the number of students in each Verbal SAT score interval. . The proportion is the ratio of the frequency for each interval to the total frequency.
3. The percentage is the proportion multiplied by100.
4. The total frequency can be calculated by adding up all the frequencies in the table.

STEP 2

First, we need to calculate the total frequency. We can do this by adding up all the frequencies in the table.
$Total\, frequency = \sum f$

STEP 3

Now, plug in the given values for the frequencies to calculate the total frequency.
$Total\, frequency =17 +22 +15 + +2$

STEP 4

Calculate the total frequency.
$Total\, frequency =17 +22 +15 +4 +2 =60$

STEP 5

Now that we have the total frequency, we can calculate the proportion for the $600-699$ interval. The proportion is the ratio of the frequency for this interval to the total frequency.
$Proportion = \frac{f}{Total\, frequency}$

STEP 6

Plug in the values for the frequency of the $600-699$ interval and the total frequency to calculate the proportion.
$Proportion = \frac{22}{60}$

STEP 7

Calculate the proportion for the $600-699$ interval.
$Proportion = \frac{22}{60} =0.37$

STEP 8

Now that we have the proportion for the $600-699$ interval, we can calculate the percentage. The percentage is the proportion multiplied by100.
$Percentage = Proportion \times100$

STEP 9

Plug in the value for the proportion of the $600-699$ interval to calculate the percentage.
$Percentage =.37 \times100$

STEP 10

Calculate the percentage for the $600-699$ interval.
$Percentage =0.37 \times100 =37 \%$

STEP 11

Now we need to calculate the proportion for the $500-599$ interval. The proportion is the ratio of the frequency for this interval to the total frequency.
$Proportion = \frac{f}{Total\, frequency}$

STEP 12

Plug in the values for the frequency of the $500-599$ interval and the total frequency to calculate the proportion.
$Proportion = \frac{15}{60}$

STEP 13

Calculate the proportion for the $500-599$ interval.
$Proportion = \frac{15}{60} =0.25$

STEP 14

Now that we have the proportion for the $500-599$ interval, we can calculate the percentage. The percentage is the proportion multiplied by100.
$Percentage = Proportion \times100$

STEP 15

Plug in the value for the proportion of the $500-599$ interval to calculate the percentage.
$Percentage =0.25 \times100$

STEP 16

Calculate the percentage for the $500-599$ interval.
$Percentage =0.25 \times100 =25 \%$ The completed table is\begin{tabular}{llll}Score Interval & f & Proportion & Percentage \\ \hline $700-799$ & &0.28 & $28 \%$ \\ $600-699$ &22 &0.37 & $37 \%$ \\ $500-599$ &15 &0.25 & $25 \%$ \\ $400-499$ &4 &0.07 & $\%$ \\ $300-399$ &2 &0.03 & $3 \%$ \end{tabular}

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