The tutor shows a convenient way to estimate the standard deviation.

Let’s imagine the following list of 20 test scores:

43, 44, 49, 51, 52, 55, 57, 58, 61, 64, 68, 73, 74, 76, 77, 82, 84, 85, 87, 91

Of course, you could easily get the standard deviation, mean, etc from a calculator (see my statistics category). However, there is a shortcut method that involves dividing the numbers into ranges, then using frequencies:

Step 1: Write the numbers in ascending order. (The list above is already that way.)

Step 2: Organize the numbers into separate ranges – I usually use four or five:

Step 3: Now, find the standard deviation as if the list consists of each range midpoint, represented by its frequency. The above list becomes

47.5 (freq: 5), 57.5 (freq: 4), 67.5 (freq: 2), 77.5 (freq: 5), 87.5 (freq: 4)

Each calculator I’m familiar with has a shortcut way to enter frequencies. Today, we’ll cover the Casio fx-260Solar (see my post here for more detail):

Step 1: Press mode then . (decimal point) to get into SD mode.

Step 2: To enter 47.5 five times, key in 47.5 X 5, then press the M+ key.

Step 3: Continue by keying 57.5 X 4 M+ and so on.

Step 4: Once you’ve worked through the list, press shift then 6. You should recieve the answer 20, meaning you have entered 20 data values.

Step 5: Press shift 8 for σ_n or shift 9 for σ_n-1, whichever standard deviation is desired.

From my experience, σ_n is preferred in high school, while σ_n-1 is more often used at post-secondary level. If you’re not sure which to use, ask your instructor.

Here are the answers you hopefully receive. Note also the standard deviation without the shortcut:

You can see how close the shortcut values are to the real values.

Note: to get out of SD mode, press mode 0

Even greater advantage from the frequency method can be realized when calculating standard deviation by hand. I’ll be talking more about that in a future post.

HTH:)

Source:

Casio fx-260Solar User’s Guide

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.