Data Science and A.I.: Measures of Dispersion – Variance of Continuous Frequency Distribution**
Introduction
“Hey there, welcome to PostNetwork Academy, your go-to place for all things Data Science and AI! Before we jump into today’s lesson, make sure to check out our website at [postnetwork.co](https://postnetwork.co), YouTube channel, Facebook page, and LinkedIn for all the latest updates. Alright, now you’re connected, let’s get started with today’s topic: calculating the variance of continuous frequency distribution. If you are working with statistics, data science, or AI, this is a technique you will use regularly. Variance measures how spread out data points are in a dataset.”
Variance
“When working with continuous frequency distributions, calculating variance involves a few extra steps, but don’t worry! We will go through it step by step. So, what is variance? Variance is a measure of the dispersion of data points in a dataset. By the end of this video, you will be able to confidently calculate variance for any continuous dataset you come across. So, let’s dive into an example. Here’s a table with class intervals and frequencies. The first thing we need to calculate is the midpoint for each class interval, also called the ‘mid-values’.”
Calculating Variance
“To calculate mid-values, you add the lower limit and the upper limit, then divide by two. For example, the midpoint between 0 and 1,000 is 500. The next midpoint, between 1,000 and 2,000, is 1,500. Similarly, the third is 2,500, the fourth is 3,500, and so on. Now, to calculate \( u_i \), we use the formula: \( u_i = \frac{x_i – A}{h} \), where A is the assumed mean and h is the class interval width.”
“In this example, we are using 2,500 as the assumed mean and 1,000 as the class interval width. For the first class, where the midpoint is 500, \( u_i = \frac{500 – 2,500}{1,000} = -2 \). For the second class, with a midpoint of 1,500, \( u_i = -1 \). You can calculate the rest similarly.”
“Next, we calculate the product of the frequency (\( f_i \)) and \( u_i \) for each class. For the first entry, \( f_i = 18 \) and \( u_i = -2 \), so \( f_i u_i = -36 \). For the second entry, \( f_i u_i = -26 \), and so on. Now, square the \( u_i \) values to get \( u_i^2 \), and multiply the frequencies by these squared values. For the first class, \( f_i = 18 \) and \( u_i^2 = 4 \), so \( f_i u_i^2 = 72 \). Continue this for the rest of the data.”
“After calculating all the values, we add up \( f_i u_i^2 \) to get 186. We also calculate the sum of \( f_i u_i \), which is -18. Now, using the variance formula:
\[ Var(X) = h^2 \left( \frac{1}{N} \sum f_i u_i^2 – \left( \frac{1}{N} \sum f_i u_i \right)^2 \right) \]
We plug in the values and find the variance to be 1,827,600.”
“This was an example of how to calculate the variance of a continuous frequency distribution. Hope you’ve understood it! Thanks for watching the video.”
Key Takeaways:
– Learn how to calculate variance for continuous frequency distributions using mid-values and \( u_i \) values.
– Apply the variance formula step-by-step to get the correct result.
– Practice using this technique in your data science and AI projects.
Video
PDF Presentation
var cfd ex 2For more tutorials on data science and AI, subscribe to our YouTube channel and follow us on social media for updates:
– [Website](https://postnetwork.co)
– [YouTube](https://www.youtube.com/@postnetworkacademy)
– [Facebook](https://www.facebook.com/postnetworkacademy)
– [LinkedIn](https://www.linkedin.com/company/postnetworkacademy)