Answers to Problems 5 through 8
Let's do this on your Casio 300W
The statistical functions of your calculator can save you from doing lots of monotonous, repetitious busy work.
Please have your calculator with you as you work through these problems.
Modes:
Press the [ON] button.
Press [MODE] once and you should see:
Entering Data:
This section assumes your calculator is in SD mode. Before we begin, I want you to locate the data entry key [M+] on your calculator. It is the button just above the read [AC] button. It is also important that you do not confuse the negative button [(-)] on the left side of your calculator with the subtraction button which is on the lower right side of your calculator. The negative button [(-)], just above the [STO] button, is used to enter negative numbers. The subtraction button [–], just above the [=] button, is not used for data entry.
Before you enter new data into your calculator, it is important that you clear the statistical memories.
Press [SHIFT] [AC] [=]
Your screen will show SCL for "Statistical Clear." Don't worry, this will disappear when we start entering data. If you don't see SCL on your screen Press [SHIFT] [AC] [=] again until you do.. Here is our data again:
Score |
Freq. |
22 |
1 |
21 |
2 |
20 |
1 |
19 |
0 |
18 |
1 |
17 |
4 |
16 |
4 |
15 |
7 |
14 |
4 |
13 |
1 |
The general form for entering frequency data is to enter the value then [SHIFT] [,] then the frequency then [M+]. 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 [SHIFT] [,] is treated as if the frequency is 1.
Press [2] [2] [SHIFT] [,] [1] [M+]
Before pressing the [M+] your display will say 12;1, (the [SHIFT] [,] becomes a semicolon. When you press the [M+] your display will say 12 (the value). |
[2] [1] [SHIFT] [,] [2] [M+]
[2] [0] [SHIFT] [,] [1] [M+]
[1] [9] [SHIFT] [,] [0] [M+]
[1] [8] [SHIFT] [,] [1] [M+]
[1] [7] [SHIFT] [,] [4] [M+]
[1] [6] [SHIFT] [,] [4] [M+]
[1] [5] [SHIFT] [,] [7] [M+]
[1] [4] [SHIFT] [,] [4] [M+]
[1] [3] [SHIFT] [,] [1] [M+]
Do NOT clear your calculator until we start problem #9. If you do clear your calculator before then, you will need to re-enter all of the above data.
Now we can start working the problems
5. If Data Set A is an entire population, what is its mean (μ)?
To obtain the Population mean, press:
[SHIFT] [1] [=] Your display should read 16.32
6. If Data Set A is an entire population, what is its variance (σ^{2})?
To get the population variance, you need to square the population standard deviation. Because you have already enter the data, so all you need to do to calculate the population standard deviation is to press:
[SHIFT] [2] [=] Your display should read 2.361694307
To square this value to get the variance, press [X^{2}] Your display should read 5.5776
7. If Data Set A is a randomly selected sample from a larger population, what is the mean ()?
To obtain the sample mean, press:
[SHIFT] [1] [=] Your display should read 16.32
yup - the population mean and sample mean are computed the same way.
Now that we have the mean, we can revisit problem #4. Are the data in Data Set A skewed? If so, are they positively or negatively skewed? The median is 16 and the mean is 16.32. As the mean is greater than the median, this data is positively skewed.
8. If Data Set A is a randomly selected sample from a larger population, what is its variance (s^{2})?
To calculate the sample standard deviation is to press:
[SHIFT] [3] [=] Your display should read 2.410394159
To square this value to get the variance, press [X^{2}] Your display should read 5.81.