Standard Deviation of Continuous Grouped Data
For the continuous grouped data we can easily calculate the standard deviation using the Discrete data formulas by replacing each class with its midpoint (as xi) and then normally calculating the formulas.
Midpoint of each class is calculated using formula,
xi (Midpoint) = (Upper Bound + Lower Bound)/2
For example, Calculate standard deviation of continuous grouped data as given in table,
Class | 0-10 | 10-20 | 20-30 | 30-40 |
---|---|---|---|---|
Frequency(fi) | 2 | 4 | 2 | 2 |
Actual Mean Method
- Assumed Mean Method
- Step Deviation Method
We can use any of above methods to find the standard deviation. Here we find standard deviation using the actual mean method.
Solution to above question is,
Class | 5-15 | 15-25 | 25-35 | 35-45 |
---|---|---|---|---|
xi | 10 | 20 | 30 | 40 |
Frequency(fi) | 2 | 4 | 2 | 2 |
Mean (x̄) = ∑(fi xi)/∑(fi)
⇒ Mean (μ) = (10×2 + 20×4 + 30×2 + 40×2)/(2+4+2+2)
⇒ Mean (μ) = 240/10 = 24
n = ∑(fi) = 2+4+2+2 = 10
xi | fi | fixi | (xi – x̄) | (xi – x̄)2 | fi(xi – x̄)2 |
---|---|---|---|---|---|
10 | 2 | 20 | 14 | 196 | 392 |
20 | 4 | 80 | -4 | 16 | 64 |
30 | 2 | 60 | 6 | 36 | 72 |
40 | 2 | 80 | 16 | 256 | 512 |
Now,
σ = √(∑in fi(xi – x̄)2/n)
⇒ σ = √[(392 + 64 + 72 +512)/10]
⇒ σ = √(104) = 10.198
Standard Derivation(σ) = 10.198
Similarly, other methods can also be used to find standard deviation of continuous grouped data.
Standard Deviation – Formula, Examples & How to Calculate
Standard Deviation is the measure of the dispersion of statistics. The standard deviation formula is used to find the deviation of the data value from the mean value i.e. it is used to find the dispersion of all the values in a data set to the mean value. There are different standard deviation formulas to calculate the standard deviation of a random variable.
In this article, we will learn about what is standard deviation, the standard deviation formulas, how to calculate standard deviation, and examples of standard deviation in detail.
Table of Content
- What is Standard Deviation?
- Standard Deviation Definition
- Standard Deviation Formula
- Formula for Calculating Standard Deviation
- How to Calculate Standard Deviation?
- What is Variance
- Difference between Variance and Deviation
- Varience Formula
- How to Calculate Variance?
- Standard Deviation of Ungrouped Data
- Standard Deviation of Discrete Grouped Data
- Standard Deviation of Continuous Grouped Data
- Standard Deviation of Probability Distribution
- Standard Deviation of Random Variables
- Standard Deviation Formula Example
- Standard Deviation Formula Excel
- Standard Deviation Formula Statistics