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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.

Entering Data (Part 1):

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
23
-5
14
4

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 9.6

Before 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.

Practice Opportunity:

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.

Practice Opportunity:

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.


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