Relative Frequency Histogram - GeeksforGeeks (2024)

A histogram in mathematics is a graphical representation of data using a bar graph. The height of each bar graph points to the frequency of the data point in a particular range, which makes it easy to visualize the data. They are used in a wide number of fields including statistics, data analysis etc.

In this article, we’ll study about relative frequency histograms.

Histogram Definition

A histogram is defined as,

A histogram is a type of bar graph that shows the frequency of different ranges of data values in a dataset. It helps to visualize the distribution of the data. Each bar in a histogram represents a range (or “bin”) of values, and the height of the bar shows how many data points fall within that range.

For a histogram,

• Data Range: Entire range of data is divided into smaller, equal-sized intervals, called bins.

• Counting Data Points: Count how many data points fall into each bin.

• Drawing Bars: Draw a bar for each bin. The height of each bar represents the number of data points in that bin.

Example of histogram, consider the following data:

(Here, height range is the data range, number of trees( frequency) is the data count and below is the histogram.)

Histogram for above data:

Relative Frequency Histogram

A relative frequency histogram is a type of bar graph that shows how often different values happen in a data set, but instead of showing the actual number of times each value occurs, it shows the proportion or percentage of the total number of values.

What is Relative Frequency?

Formula for relative frequency is:

Relative Frequency = (Number of Successful Trials)/(Total Number of Trials)

How to Make a Relative Frequency Histogram?

To make a relative frequency histogram follow the steps added below:

• Step 1: Data Collection: First, you gather your data. For example, let’s say you’re recording the heights of students in your class.

• Step 2: Divide into Intervals: You split the range of data (heights) into equal-sized intervals or bins. For instance, you might have bins for heights from 140-150 cm, 150-160 cm, and so on.

• Step 3: Count Occurrences: Count how many data points (students’ heights) fall into each bin.

• Step 4: Calculate Relative Frequencies: Instead of just counting, you divide the count of each bin by the total number of data points. This gives you a proportion or percentage. For example, if there are 10 students in the 140-150 cm bin and 50 students in total, the relative frequency is 10/50 = 0.2 or 20%.

• Step 5: Draw Histogram: On the horizontal axis (x-axis), you put the bins. On the vertical axis (y-axis), you put the relative frequencies. Each bin is represented by a bar whose height corresponds to its relative frequency.

Formula to Calculate Relative Frequency

Formula to calculate the relative frequency of a data point in a specific interval is:

f_i = n_i / N

where:

• n_i is the Frequency of Data Points in Interval
• N is the Total Number of Data Points

This formula computes the proportion or percentage of data points in a particular interval relative to the total number of data points in the dataset. The resulting relative frequencies are then used to construct the relative frequency histogram.

Multimodal Vs Symmetric Distribution

A multimodal distribution has more than one high point or peak. It’s like a graph with multiple mountains, whereas, A symmetric distribution has one peak in the middle, and the left and right sides look the same. It’s like a single, balanced hill.

Multimodal Distribution Graph

Symmetric Distribution Graph

Examples on Relative Frequency Histogram

Example 1: Suppose we have distribution of daily wages (in ₹) for a group of workers, and how does it vary across different wage ranges?

Solution:

Calculation of Relative Frequency:

Total number of workers: 10 + 20 + 40 + 16 + 8 + 6 = 100

Now,

For the interval 30-40:

Frequency: 10

Relative frequency: f= 10/100 = 0.10

For the interval 40-50:

Frequency: 20

Relative frequency: f= 20/100 = 0.20

For the interval 50-60:

Frequency: 40

Relative frequency: f= 40/100 = 0.40

For the interval 60-70:

Frequency: 16

Relative frequency: f= 16/100 = 0.16

For the interval 70-80:

Frequency: 8

Relative frequency: f= 8/100 = 0.08

For the interval 80-90:

Frequency: 6

Relative frequency: f= 6/100 = 0.06

Relative Frequency Histogram:

Example 2: Construct a relative frequency histogram using provided dataset?

Solution:

Calculation of Relative Frequency:

Total number of workers: 30+25+45+15+20+40 = 175

Now,

For the interval 50-60:

Frequency: 30

Relative frequency: f= 30/175 =0.17

For the interval 60-70:

Frequency: 25

Relative frequency: f= 25/175 =0.14

For the interval 70-80:

Frequency: 45

Relative frequency: f= 45/175 =0.26

For the interval 80-90:

Frequency: 15

Relative frequency: f= 15/175 =0.085

For the interval 90-100:

Frequency: 20

Relative frequency: f= 20/175 =0.114

For the interval 100-110:

Frequency: 40

Relative frequency: f= 40/175 =0.23

Relative Frequency Histogram:

Example 3: Construct a relative frequency histogram using provided dataset?

Solution:

Calculation of Relative Frequency:

Total number of workers: 12+18+15+9+8 = 62

Now,

For the interval 40-45:

Frequency: 12

Relative frequency: f= 12/62 =0.19

For the interval 45-50:

Frequency: 18

Relative frequency: f= 18/62 =0.29

For the interval 50-55:

Frequency: 15

Relative frequency: f= 15/62 =0.24

For the interval 55-60:

Frequency: 9

Relative frequency: f = 9/62 = 0.15

For the interval 60-65:

Frequency: 8

Relative frequency: f = 8/62 = 0.13

Relative Frequency Histogram:

Conclusion

In conclusion, relative frequency histograms are a useful tool for understanding data. They show us how data is spread out in an easy-to-see way. People use these graphs in many fields, like science, business, and healthcare, to see patterns and make good decisions. Because they show data as percentages, it’s easy to compare different sets of data. This helps people find areas to improve and create better strategies.

FAQs on Relative Frequency Histogram

What is a Relative Frequency Histogram?

Relative frequency histogram is a type of bar graph that shows the proportion or percentage of data points that fall into different ranges or bins. Instead of showing how many times something happens, it shows how often it happens compared to the total number of data points.

How is Relative Frequency Histogram different from a Regular Histogram?

• Regular histogram shows the actual number of times something happens in each bin.
• Relative frequency histogram shows the proportion or percentage of the total that each bin represents. It’s like looking at how big each part is compared to the whole.

Why do we use Relative Frequency Histograms?

We use relative frequency histograms to easily compare different data sets, even if they have different total numbers of data points. It helps us understand the distribution of data as percentages, which can be more useful in some cases.

How to Make a Relative Frequency Histogram?

To make relative frequency histogram follow the steps added in the article above.