# How Can I Calculate Standard Deviation (step-by-step) in R? [closed]

How can I calculate Standard Deviation, step-by-step, in R? Thanks!

• Do you know the formula for standard deviation? Can you elaborate on 'step by step'? Sep 11, 2015 at 2:46
• Hi! Yes, I believe do! I'm trying to calculate sd for a specific data set. I am aware that I can simply use the sd function, but I need to calculate the standard deviation of a data set "by hand," using R. These are the values:  179 160 136 227 217 168 108 124 143 140 309 229 181 141 260 203 148 169 213 257 244  271 243 230 248 327 329 250 193 271 316 267 199 171 158 248 423 340 392 339 341 226  320 295 334 322 297 318 325 257 303 315 380 153 263 242 206 344 258 368 390 379 260  404 318 352 359 216 222 283 332 Thank you! Sep 11, 2015 at 2:56
• $variance = \frac{sum((x-mean(x))^2)}{(length(x)-1)}$ Sep 11, 2015 at 3:07

> a <- c(179,160,136,227)
> sd(a)
 38.57892
> sqrt(sum((a-mean(a))^2/(length(a)-1)))
 38.57892




So, you want to calculate the standard deviation step-by-step. So, firstly, you should calculate the sum of the differences of all data points with the mean.

Have a variable called count and set it to the value 0.

For that, you loop through the data set with a variable, say i and subtract i every time with the mean. Mean can be calculated as mean(dataset).

Add the result of every loop iteration to count, by count = count + (i-mean)^2

Now, divide the count variable by len(dataset) - 1

The result is the variance. So, for calculating the standard deviation, you have to square root the above value.

In R, you do this as: sqrt(variance)`

Finally, the result you get after applying the square root is the Standard Deviation.

• "+=" is not an operator in R Sep 12, 2015 at 5:55
• Glen_b Thank you. Edit done. Was going with the pseudo algo format. Sep 12, 2015 at 6:47