Proportional Data Math Example 1

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Example 1

easy
In a survey, 45 out of 180 students prefer online learning. Calculate the sample proportion p^\hat{p} and interpret it.

Solution

  1. 1
    Sample proportion formula: p^=xn\hat{p} = \frac{x}{n}
  2. 2
    Substitute: p^=45180=0.25\hat{p} = \frac{45}{180} = 0.25
  3. 3
    Convert to percentage: 0.25×100=25%0.25 \times 100 = 25\%
  4. 4
    Interpret: 25% of sampled students prefer online learning; this estimates the true population proportion

Answer

p^=45180=0.25=25%\hat{p} = \frac{45}{180} = 0.25 = 25\%
Sample proportion p^=x/n\hat{p} = x/n is the fundamental estimate of a population probability from data. It is always between 0 and 1. The sample proportion is an unbiased estimator of the true population proportion pp.

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 →

More Proportional Data Examples

Example 2 medium

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

Example 3 easy

In a class of 25 students, 15 passed the test. Calculate [formula] and find the number expected to p

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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