How to Make a Frequency Table for a Histogram?

Creating a frequency table is the first step in making a histogram. It involves organizing raw data into meaningful intervals (bins) and counting how many data points fall within each interval.

Here's a breakdown of how to make a frequency table for a histogram:

1. Determine the Range: Find the highest and lowest values in your dataset. Subtract the lowest value from the highest value to calculate the range.

2. Decide on the Number of Bins (Classes/Intervals): There's no fixed rule, but generally, use between 5 and 20 bins. The number of bins depends on the size and distribution of your data. A larger dataset may benefit from more bins. Use Sturges' Rule as a guide: Number of bins ≈ 1 + 3.322 * log(n), where 'n' is the number of data points.

3. Calculate the Bin Width: Divide the range by the desired number of bins to determine the bin width. Bin Width = Range / Number of Bins. Round the bin width up to a convenient number.

4. Define the Bin Boundaries (Class Limits):

   • Start with the lowest value in your dataset (or a slightly lower convenient value).
   • Add the bin width to the starting value to get the upper boundary of the first bin.
   • The upper boundary of the first bin becomes the lower boundary of the second bin.
   • Repeat until you've created all the bins, ensuring the highest value in your dataset is included within the last bin.

5. Tally the Frequencies: Go through your dataset and count how many data points fall into each bin. This is the frequency for that bin. Be consistent with how you handle values that fall exactly on a bin boundary (e.g., always include them in the lower bin).

6. Create the Frequency Table: Organize the bins (intervals) and their corresponding frequencies into a table.

Example:

Let's say you have a dataset of student test scores: 62, 65, 71, 73, 75, 78, 82, 85, 88, 91, 94, 96.

1. Range: 96 - 62 = 34

2. Number of Bins: Let's choose 4 bins for simplicity.

3. Bin Width: 34 / 4 = 8.5. Round up to 10.

4. Bin Boundaries:

   • 60-69
   • 70-79
   • 80-89
   • 90-99

5. Tally the Frequencies:

   • 60-69: 2 (62, 65)
   • 70-79: 4 (71, 73, 75, 78)
   • 80-89: 3 (82, 85, 88)
   • 90-99: 3 (91, 94, 96)

6. Frequency Table:

Bin (Score Range)	Frequency
60-69	2
70-79	4
80-89	3
90-99	3

This frequency table can then be used to create a histogram, where the x-axis represents the bins (score ranges) and the y-axis represents the frequencies.