You will find the functions mean and stdDev on the TI-83/84 located in 2nd LIST MATH 3, and 7.
They operate on lists, so create a list, for example,
randInt(-5,9,23)→L1 ENTER
{-1 5 -1 2 5 9 ...} ** my numbers **
This is a list of 23 numbers between -5 and 9.
mean(L1) computes the average of L1
Two methods of computing the average are:
sum(L1)/23 ENTER (sum is located in 2nd LIST MATH 5.)
2.565217391
mean(L1) ENTER
2.565217391
Your numbers can be different from mine, but they will also be equal to each other.
The standard deviation estimates the expected deviation of individual items from their average.
A step by step computation of the standard deviation:
L1-mean(L1)→L2 ** subtracts the average from each number in L1**
{-3.565217391 2 ...
L22→L2 ENTER ** computes the squares of the numbers in L2**
{12.71077505 5. ...
sum(L2) ENTER ** computes the sum of squares **
99.6521739
ANS/22 ENTER ** computes the average of squares using the number of items minus 1 **
13.262055336
σ(ANS) ENTER ** computes the standard deviation **
3.690603387
A simple computation of the standard deviation:
stdDev(L1) ENTER
3.690603387
Remark: Dividing by the number of items minus 1 gives a better estimate of the deviation from average for short lists.
Still another approach.
Use STAT CALC 1:1-Var Stats
1-Var Stats L1 ENTER
You get lots of numbers,
x bar is the mean;
Σx is the sum of the list (Σ is the Greek letter capital sigma)
Σx2 is the sum of the squares of the list
n is the length of the list (here 23);
Sx gives you the standard deviation as you computed it;
Σx computes the standard deviation by dividing the sum of squares by n = 23, and not by 22.
Check the difference by computing,
sum(L2)/23
13.02835539
√ (ANS)
3.609481318
Remark
In most situations it doesn't matter how you compute the standard deviation (dividing by n or dividing by n-1).