So this table is all about showing you how to calculate the standard deviation in various steps.
Step 1: calculate the average (=mean) of the x values. You probably know how to do this, add all values and divide by the number of values. (53+51+48+49+37)/5 = 47.6. This is your [tex]\overline{x}[/tex].
Step 2: calculate [tex]x - \overline{x}[/tex]. This is the "distance" of your x value to the average. This has been done for you already in the second column. E.g. 53-47.6=5.4.
Step 3: square the results of [tex]x - \overline{x}[/tex]. This is also done for you already, it is the third column.
Step 4: Add (sum) the [tex](x - \overline{x})^2[/tex] values. So add the third column. I get 155.2 when I do that.
Step 5: Divide that sum by the number of x values. 155.2/5 = 31.04 ≈ 31. That number is your variance right there!
Step 6: Take the square root of the variance. √31.04 ≈ 5.571 ≈ 5.6. This is your standard deviation.
