Data Science and A.I. Lecture Series: Computing the 70th Percentile

Welcome to our Data Science and A.I. lecture series! In this post, we’ll cover a fundamental concept in statistics – percentiles. Specifically, we’ll learn how to compute the 70th percentile, or P₇₀, for a grouped data set.

Understanding Percentiles

Percentiles divide a data set into 100 equal parts, giving us a way to understand the distribution of values. For instance, the 70th percentile represents the value below which 70% of the data falls. Here, we’ll calculate P₇₀ using a frequency distribution table.

Data Table

The table below shows the class intervals (C.I.) and their corresponding frequencies (f_i):

C.I.	fi	Cumulative Frequency (C.F.)
0-10	5	5
10-20	7	12
20-30	10	22
30-40	16	38
40-50	11	49
50-60	7	56
60-70	5	61
70-80	4	65
80-90	3	68
90-100	2	70

Steps to Compute P₇₀

To find P₇₀, we’ll use the formula:

P₇₀ = l + [(N × 70 / 100) – F] / f × h

• l = lower boundary of the class containing P₇₀
• N = total frequency, which is 70
• F = cumulative frequency just before the 70th percentile class
• f = frequency of the 70th percentile class
• h = class interval width, which is 10

Calculation

1. First, calculate (N × 70) / 100:

(70 × 70) / 100 = 49

2. Look for the cumulative frequency just greater than 49, which is 56. This makes the 50-60 class the 70th percentile class.

3. Substitute the values into the formula:

l = 50, F = 49, f = 7, h = 10

P₇₀ = 50 + [(49 – 49) / 7] × 10

This simplifies to:

P₇₀ = 50

PDF Presentation

percentilegrouped

Video

Conclusion

So, the 70th percentile for this data set is 50. Percentiles are essential for understanding data distribution and are widely used in data science and A.I.

Thank you for reading this post in our Data Science and A.I. lecture series. Stay tuned for more insights into the world of data!