Table of Content

• Histogram Definition
• Relative Frequency Histogram
• What is Relative Frequency?
• How to Make a Relative Frequency Histogram?
• Formula to Calculate Relative Frequency
• Multimodal Vs Symmetric Distribution
• Multimodal Distribution Graph
• Symmetric Distribution Graph
• Examples on Relative Frequency Histogram

(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.

Aspect	Multimodal Distribution	Symmetric Distribution
Definition	Has more than one peak or high point	Has one central peak with mirrored sides
Example	Favorite sports of different grades (e.g., soccer and basketball)	Test scores where most are around the average
Appearance	Looks like multiple mountains or bumps	Looks like a single, balanced hill
Peaks	Several peaks	One central peak
Shape	Irregular with multiple high points	Regular, mirror-image shape
Data Interpretation	Indicates multiple groups or popular choices	Indicates a balanced spread around the center
Real-World Example	Heights of students from different schools	Heights of students in one class
Typical Distribution	Multiple local maximum points in the data	Symmetric around the central value

Multimodal Distribution Graph

Multimodal Distribution Graph

Symmetric 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?

Wage Range (₹)	30 -40	40 – 50	50 – 60	60 – 70	70- 80	80 – 90
Number of Workers	10	20	40	16	8	6

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:

Wage Range (₹) X	30 – 40	40- 50	50 – 60	60 – 70	70 – 80	80 – 90
Number of Workers [Relative Frequency Range] Y	0.10	0.20	0.40	0.16	0.08	0.06

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

Class Intervals	50 – 60	60 -70	70 – 80	80 – 90	90 – 100	100 – 110
Frequency	30	25	45	15	20	40

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:

Class Intervals	50 – 60	60- 70	70 – 80	80 – 90	90 – 100	100 – 110
frequency	0.17	0.14	0.26	0.085	0.114	0.23

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

Height ( in cm)	40-45	45-50	50-55	55-60	60-65
Number of Boys	12	18	15	9	8

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:

Height (in cm)	40 – 45	45-50	50-55	55-60	60-65
Number of Boys	0.19	0.29	0.24	0.15	0.13

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.