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Statistics and Probability - Relative frequency

Grade 10IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Relative frequency is the ratio of the number of times a particular event occurs to the total number of trials conducted in an experiment.

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It is also known as experimental probability because it is based on observed data rather than theoretical reasoning.

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As the number of trials (nn) increases, the relative frequency tends to get closer to the theoretical probability of the event. This is known as the Law of Large Numbers.

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The sum of the relative frequencies for all possible outcomes in an experiment is always 11.

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Relative frequency can be expressed as a fraction, a decimal, or a percentage, and it always lies in the range 0≤Relative Frequency≤10 \le Relative\ Frequency \le 1.

📐Formulae

Relative Frequency=Frequency of the event (f)Total number of trials (n)Relative\ Frequency = \frac{\text{Frequency of the event (f)}}{\text{Total number of trials (n)}}

∑Relative Frequency=1\sum Relative\ Frequency = 1

Estimated Number of Occurrences=Relative Frequency×Total Number of Trials\text{Estimated Number of Occurrences} = Relative\ Frequency \times \text{Total Number of Trials}

💡Examples

Problem 1:

A spinner with four colors (Red, Blue, Green, Yellow) is spun 200200 times. The results show that the color Blue appeared 4646 times. Calculate the relative frequency of the spinner landing on Blue.

Solution:

Relative Frequency(Blue)=46200=0.23Relative\ Frequency (Blue) = \frac{46}{200} = 0.23

Explanation:

To find the relative frequency, divide the frequency of the specific outcome (Blue = 4646) by the total number of trials (200200). The result is 0.230.23 or 23%23\%.

Problem 2:

The relative frequency of a computer component failing within the first year is found to be 0.050.05. In a batch of 25002500 components, how many are expected to fail?

Solution:

Expected failures=0.05×2500=125\text{Expected failures} = 0.05 \times 2500 = 125

Explanation:

Multiply the relative frequency (the probability based on past data) by the total number of units in the batch to estimate the number of occurrences.

Problem 3:

A student flips a coin 5050 times and records 2828 Heads. Calculate the relative frequency of Tails.

Solution:

Frequency of Tails=50−28=22\text{Frequency of Tails} = 50 - 28 = 22 Relative Frequency(Tails)=2250=0.44Relative\ Frequency (Tails) = \frac{22}{50} = 0.44

Explanation:

First, find the frequency of Tails by subtracting the number of Heads from the total trials. Then, divide the frequency of Tails by the total trials (5050) to get 0.440.44.