|
||||
Stat Tutorials |
||||
|
|
|
|
|
Jump to: Modes Entering Data Calculating the Mean, Standard Deviation, and Variance Entering Frequency Data Practice Opportunity 1 Practice Opportunity 2
Using Your Sharp EL-531R Calculator - Single-Variable Statistics
With very little effort you can learn to use your calculator to calculate a number of important single-variable statistics.
Objectives
By the end of this learning activity, you will be able to:
Please make sure you have your calculator at hand.
The statistical functions of your calculator can save you from doing days and days of monotonous, repetitious busy work.
Modes:
Notice that above the [DRG] button it says "MODE" in yellow. Your calculator is always in one of three modes: normal, one-variable statistics, or two-variable statistics. Press [2ndF] [DRG] and your calculator will ask if you want mode 0, mode 1, or mode 2. Press [1]. Notice that now your calculator screen has a black rectangle with the "STAT" written in light gray in the rectangle. That rectangle tells you that your calculator is in one of the two statistical modes (either one-variable or two-variable). The absence of that rectangle tells you that you are in normal mode. We will use the one-variable statistical mode (mode 1) for this lesson.
This section assumes your calculator is in SD mode. Before we begin, I want you to locate a few couple of keys on your calculator. The data entry key [M+] is the button just above the [ )] button. The recall button [RCL] is just above the [9] and the [( ] buttons.
It is also important that you do not confuse the negative button [+/-] with the subtraction button. The negative button [+/-], just below the [3] button, is used to enter negative numbers. The subtraction button [–], just above the [=] button, is not used for data entry.
Let's imagine you want to find the mean, standard deviation, and variance of the following data:
12 |
Before you enter new data into your calculator, it is important that you clear the statistical memories.
Press [2ndF] [DEL]
Let's enter that data now:
[
1] [2] [M+][
2] [3] [M+][
+/-] [5] [M+] it is important that you press the negative button, not the subtraction button.[
1] [4] [M+][
4] [M+]That's it!! Wasn't that easy? We only need to enter the data once, and as long as we do not clear our calculator, we can ask our calculator to compute a number of different statistics (or parameters) based on that data.
Calculating the Mean, Standard Deviation, and Variance:
To obtain the mean press:
[
RCL] [4] Your display should read 9.6Before calculating the standard deviation and variance, you need to determine if your data constitutes the entire population or just a sample of a population.
If you have the data for the entire population:
To obtain the standard deviation, press [RCL] [6]. Your display should read 9.478396489.
Once you have the standard deviation press [X2] [=] to get the variance. Your display should read 89.84.
If you have the data for only a sample:
To obtain the standard deviation, press [RCL] [5] Your display should read 10.59716943.
Once you have the standard deviation press [X2] [=] to get the variance. Your display should read 112.3.
Please note that written above [6] is σX. σ is the symbol for the population standard deviation. It is written in Greek because it is a parameter based on all the numbers in the population. Above the [5], SX is written. S is the symbol for the standard deviation of the population based only on the data from a sample. It is written in English because it is a statistic based only on the numbers in a sample.
If your display did not show the numbers above, you probably pushed the [2ndF] [DEL] buttons or the [2ndF] [DRG] when you should not have. When you press the [2ndF] [DEL] buttons or the [2ndF] [DRG] you clear out your data and need to re-enter all the data again before computing another answer based on that data. Moral to the story: Do not press those clear buttons unless you are entering a new data set.
1. What is the mean and variance of the following population.
24
74
21
-25
13
-35
Check answer by clicking here
Entering Data (Part 2) - Frequency Data
Value |
Frequency |
2 |
23 |
1 |
37 |
0 |
46 |
-1 |
102 |
-2 |
0 |
-3 |
1 |
The general form for entering frequency data is to enter the value then [,] then the frequency then [M+]. The [,] is just to the right of the [RCL] button. Because it says (x,y) in white below the key, when you are in statistical mode, you do not need to press [2ndF] to get the comma. The frequency is always positive and nonzero. If the frequency of a value is zero, just do not enter it. A value not followed by [,] is treated as if the frequency is 1.
Before entering the data, make sure your calculator is in SD mode. Clear your statistical memories by pressing [2ndF] [DEL].
[ 2] |
[ STO] |
[ 2] [3] |
[ M+] |
[ 1] |
[ STO] |
[ 3] [7] |
[ M+] |
[ 0] |
[ STO] |
[ 4] [6] |
[ M+] |
[ +/-] [1] |
[ STO] |
[ 1] [0] [2] |
[ M+] |
[ +/-] [2] |
[ STO] |
[ 0] |
[ M+] |
[ +/-] [3] |
[ STO] |
[ 1] |
[ M+] |
Value |
, |
Frequency |
Enter |
Press [RCL] [4] and your display will tell you that the mean is -0.105263158.
2. What is the variance and mean of the population from which the following data was sampled:
Value |
Frequency |
27 |
102 |
13 |
1 |
0 |
7 |
-12 |
13 |
24 |
0 |
-39 |
6 |
Check answer by clicking here.
That is it for the calculator until we get into bivariate statistics.