Practice Proportional Data in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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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

easy
In a class of 4040 students, 35%35\% play an instrument. How many students is that?

Example 2

medium
Of 1,2001{,}200 ticket holders, 54%54\% are season members. How many ticket holders are NOT season members?

Example 3

medium
In a pictograph, one icon represents 2020 books. Library A shows 3.53.5 icons and Library B shows 55 icons. What proportion of the combined collection is in Library A?

Example 4

medium
A survey reports '60%60\% of voters agree' but only 55 voters were polled. Explain whether this is a meaningful summary.

Example 5

medium
A poll of 625625 adults reports p^=0.48\hat{p} = 0.48 favoring a tax measure. Estimate the standard error of p^\hat{p}.

Example 6

medium
Sales mix: product P is 30%30\% of $2M total revenue. Next year P is 40%40\% of $1.5M total. Did P's revenue rise or fall?

Example 7

medium
A stacked bar shows class spending shares: housing 40%40\%, food 25%25\%, transport 15%15\%, other 20%20\%. If total spending is $2{,}400, how much is spent on food?

Example 8

challenge
Simpson's paradox setup: hospital A treats 9090 of 100100 healthy patients and 3030 of 100100 sick patients successfully; hospital B treats 8080 of 100100 healthy and 2020 of 100100 sick. Show that A's overall rate exceeds B's, and confirm A wins within each subgroup as well.

Example 9

medium
Two pollsters report candidate support: Poll 1 says 52%52\% from 10001000 people; Poll 2 says 60%60\% from 2525 people. Which is more trustworthy and why?

Example 10

easy
Convert the proportion 3/83/8 to a percentage.

Example 11

hard
In a class, 60%60\% are girls. Of the girls, 70%70\% play sports; of the boys, 80%80\% play sports. What proportion of the entire class plays sports?

Example 12

easy
In a class of 25 students, 15 passed the test. Calculate p^\hat{p} and find the number expected to pass in a class of 100 using this estimate.

Example 13

challenge
A '200%200\% increase' is reported. Starting value is 5050. Find the new value, and explain why '200%200\% increase' differs from '200%200\% of.'

Example 14

medium
A school's lunch survey: 8080 of 400400 students chose pasta. Another school reports 2525 of 100100 students chose pasta. Which proportion is higher, and by how many percentage points?

Example 15

medium
A pictograph uses one icon =10= 10 cars. Row A shows 4.54.5 icons, row B shows 33 icons. How many cars each, and what proportion of the total is A?

Example 16

easy
A pie chart breakdown shows 35%35\% A, 25%25\% B, 15%15\% C. What percent must be 'other'?

Example 17

hard
In group A, 2020 of 5050 approve a policy (40%40\%); in group B, 3535 of 100100 approve (35%35\%). Compute the pooled approval proportion when the groups are combined.

Example 18

challenge
Two cities each report a 50%50\% approval rate. City A polled 4040 residents, City B polled 4,0004{,}000. Compare their 95%95\% margins of error (approximate z=2z=2).

Example 19

medium
Class A: 1818 of 2020 passed. Class B: 8080 of 100100 passed. Compute both proportions and state which is higher and by how many percentage points.

Example 20

hard
A retailer claims '50%50\% off' on a coat originally priced at $240, then adds a 10%10\% tax on the discounted price. Find the final price and the effective discount as a proportion of the original.
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