Proportional Data Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

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.

Solution

  1. 1
    p^=1525=0.60\hat{p} = \frac{15}{25} = 0.60
  2. 2
    Expected passes in 100 students: E=100ร—p^=100ร—0.60=60E = 100 \times \hat{p} = 100 \times 0.60 = 60 students

Answer

p^=0.60\hat{p} = 0.60; expected 60 passes in a class of 100.
Once we estimate the proportion, we can use expected count = n ร— pฬ‚ to scale to any population size. This is how actuaries, planners, and researchers project findings from samples to larger groups.

About Proportional Data

Proportional data expresses quantities as fractions or percentages of a whole, enabling fair comparison across groups of different sizes.

Learn more about Proportional Data โ†’

More Proportional Data Examples

Example 1 easy

In a survey, 45 out of 180 students prefer online learning. Calculate the sample proportion [formula

Example 2 medium

A poll finds [formula] supporting a candidate from [formula] voters. Calculate the standard error of

Example 4 hard

Compare two proportions: Group A: 30/120 support policy. Group B: 45/150 support policy. Test if the

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