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# Relative Frequency

#### Grade 7 Math Worksheets

Relative Frequency, also known as Empirical Probability, is a measure of the likelihood of an event occurring based on the observed frequency of that event in a given set of trials or observations.

• Relative Frequency
• Formula
• How to Calculate Relative Frequency?
• Solved Examples
• FAQs

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## Relative Frequency

Relative frequency, also known as empirical probability, is a measure of the likelihood of an event occurring based on the observed frequency of that event in a given set of trials or observations.

It is calculated by dividing the number of times the event occurs by the total number of trials or observations.

Relative frequency provides an estimate of the probability of an event based on observed data. It can be used to approximate the likelihood of an event when it is not possible or practical to determine the theoretical probability.

Keep in mind that as the number of trials or observations increases, the relative frequency tends to approach the true or theoretical probability.

## Formula

Relative Frequency = Number of times the event occurred / Total number of trials or observations

## How to Calculate Relative Frequency?

Step 1: Count the occurrences of the event:

Count how many times the specific event of interest occurs in your data or observations. Let’s denote this count as “N”.

Step 2: Determine the total number of trials or observations:

Count the total number of trials or observations you conducted. Let’s denote this count as “T”.

Step 3: Calculate the relative frequency:

Divide the number of occurrences (N) by the total number of trials or observations (T).

Relative Frequency = N / T

The resulting value represents the relative frequency of the event, showing the proportion or percentage of times the event occurred out of the total trials or observations.

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## Solved Example

1: Coin Toss

Suppose you toss a fair coin 100 times and record the outcomes. You observe that the coin lands on heads 60 times and tails 40 times. To calculate the relative frequency of getting heads:

Relative Frequency of Heads = 60 (number of times heads occurred) / 100 (total number of coin tosses) = 0.6 or 60%

Therefore, the relative frequency of getting heads is 0.6 or 60%.

2: Dice Roll

Consider rolling a standard six-sided die 50 times and recording the outcomes. Suppose you observe that the number 4 comes up 10 times. The relative frequency of rolling a 4 would be:

Relative Frequency of Rolling a 4 = 10 (number of times 4 occurred) / 50 (total number of dice rolls) = 0.2 or 20%

Hence, the relative frequency of rolling a 4 is 0.2 or 20%.

3: Card Drawing

Imagine drawing cards from a standard deck of 52 cards, without replacement. If you draw 20 cards and find that 6 of them are hearts, you can calculate the relative frequency of drawing a heart.

Relative Frequency of Drawing a Heart = 6 (number of hearts drawn) / 20 (total number of card draws) = 0.3 or 30%

So, the relative frequency of drawing a heart is 0.3 or 30%.

## Relative Frequency FAQS

##### What is relative frequency?

Relative frequency is a measure of how often an event occurs relative to the total number of trials or observations.

##### How is relative frequency calculated?

To calculate relative frequency, you divide the number of times an event occurs by the total number of trials or observations.

##### What does relative frequency represent?

Relative frequency represents the proportion or percentage of times an event occurred out of the total trials or observations.

##### How is relative frequency useful?

Relative frequency provides an estimate of the probability of an event based on observed data. It helps us understand how often an event occurs in relation to the total number of trials or observations.

##### Can relative frequency be greater than 1?

No, relative frequency is always between 0 and 1, or expressed as a percentage between 0% and 100%. A value of 1 or 100% indicates that the event occurred in all trials or observations.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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