Practice Proportional Data in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Proportional data expresses quantities as fractions or percentages of a whole, enabling fair comparison across groups of different sizes.
Raw counts can mislead when groups differ in size — saying "100 people in City A vs. 100 in City B have a disease" ignores that City A may be ten times larger.
Showing a random 20 of 50 problems.
Example 1
easyIn a class of students, play an instrument. How many students is that?
Example 2
mediumOf ticket holders, are season members. How many ticket holders are NOT season members?
Example 3
mediumIn a pictograph, one icon represents books. Library A shows icons and Library B shows icons. What proportion of the combined collection is in Library A?
Example 4
mediumA survey reports ' of voters agree' but only voters were polled. Explain whether this is a meaningful summary.
Example 5
mediumA poll of adults reports favoring a tax measure. Estimate the standard error of .
Example 6
mediumSales mix: product P is of $2M total revenue. Next year P is of $1.5M total. Did P's revenue rise or fall?
Example 7
mediumA stacked bar shows class spending shares: housing , food , transport , other . If total spending is $2{,}400, how much is spent on food?
Example 8
challengeSimpson's paradox setup: hospital A treats of healthy patients and of sick patients successfully; hospital B treats of healthy and of sick. Show that A's overall rate exceeds B's, and confirm A wins within each subgroup as well.
Example 9
mediumTwo pollsters report candidate support: Poll 1 says from people; Poll 2 says from people. Which is more trustworthy and why?
Example 10
easyConvert the proportion to a percentage.
Example 11
hardIn a class, are girls. Of the girls, play sports; of the boys, play sports. What proportion of the entire class plays sports?
Example 12
easyIn a class of 25 students, 15 passed the test. Calculate and find the number expected to pass in a class of 100 using this estimate.
Example 13
challengeA ' increase' is reported. Starting value is . Find the new value, and explain why ' increase' differs from ' of.'
Example 14
mediumA school's lunch survey: of students chose pasta. Another school reports of students chose pasta. Which proportion is higher, and by how many percentage points?
Example 15
mediumA pictograph uses one icon cars. Row A shows icons, row B shows icons. How many cars each, and what proportion of the total is A?
Example 16
easyA pie chart breakdown shows A, B, C. What percent must be 'other'?
Example 17
hardIn group A, of approve a policy (); in group B, of approve (). Compute the pooled approval proportion when the groups are combined.
Example 18
challengeTwo cities each report a approval rate. City A polled residents, City B polled . Compare their margins of error (approximate ).
Example 19
mediumClass A: of passed. Class B: of passed. Compute both proportions and state which is higher and by how many percentage points.
Example 20
hardA retailer claims ' off' on a coat originally priced at $240, then adds a tax on the discounted price. Find the final price and the effective discount as a proportion of the original.