Chapter 1: Sampling and Data
1.5 Using Technology for Sampling and Data
Learning Objectives
By the end of this section, the student should be able to:
- use technology to find random numbers to help create a simple random sample
This is the textbook's first Technology section. In these technology sections, technology tools will be introduced to help with the statistics concepts taught in the chapter. This section will cover tools to help generate random numbers to form a sample.
Graphing Calculator
The main tool introduced in all of these sections will be the TI-83, 83+, 84, or 84+ Graphing Calculator. Let's start with recalling some information about sampling.
As discussed in 1.2 Data, Sampling, and Variation in Data and Sampling, there are several different methods of random sampling. In each form of random sampling, each member of a population initially has an equal chance of being selected for the sample. The easiest method to describe is called a simple random sample. Any group of n individuals is equally likely to be chosen by any other group of n individuals if the simple random sampling technique is used. In other words, each sample of the same size has an equal chance of being selected.
An example was provided where Lisa wanted to form a four-person study group (herself and three other people) from her pre-calculus class, which has 31 members not including Lisa. In the section, it was shown how to use a table of random numbers to form the sample. The table used (Random Number Table) was a technology tool to generate the random numbers, but we can also do this with the graphing calculator. The problem would be set up the same way, where Lisa would list the last names of the members of her class together with a two-digit number, as in the table below:
| ID | Name | ID | Name | ID | Name |
|---|---|---|---|---|---|
| 00 | Anselmo | 11 | King | 21 | Roquero |
| 01 | Bautista | 12 | Legeny | 22 | Roth |
| 02 | Bayani | 13 | Lundquist | 23 | Rowell |
| 03 | Cheng | 14 | Macierz | 24 | Salangsang |
| 04 | Cuarismo | 15 | Motogawa | 25 | Slade |
| 05 | Cuningham | 16 | Okimoto | 26 | Stratcher |
| 06 | Fontecha | 17 | Patel | 27 | Tallai |
| 07 | Hong | 18 | Price | 28 | Tran |
| 08 | Hoobler | 19 | Quizon | 29 | Wai |
| 09 | Jiao | 20 | Reyes | 30 | Wood |
| 10 | Khan |
Generating Random Numbers on the TI-83, 83+, 84, or 84+ Graphing Calculator
To generate random numbers in the graphing calculator:
- Press MATH.
- Arrow over to PRB.
- Press 5:randInt()
This function will generate random numbers between a minimum number and a maximum number. The syntax for this function is randInt(minimum value, maximum value). For Lisa, she would use randInt(0, 30) because she assigned one class member with the lowest number of 0 and one class member with the highest number of 30. After inputting randInt(0, 30), she would press ENTER for the first random number and ENTER two more times for the other 2 random numbers. If there is a repeated value, she would press ENTER again until she had three unique numbers. Then Lisa would match the three random numbers to the three class member ID values. Below is an image of this randInt(0, 30) completed. From the list generated, the two-digit number 29 corresponds to Wai, 28 corresponds to Tran, and 04 corresponds to Cuarismo. Besides herself, Lisa’s group will consist of Wai, Tran, and Cuarismo. (Note, if you try this, you may not get the same arrangement of numbers shown, because this is a random number generator).
Lisa could have also used randInt(0, 30, 3) which would have generated 3 random numbers at once, without having to press ENTER to generate the next number.
Types of Sampling
In 1.2 Data, Sampling, and Variation in Data and Sampling, we learned about other random sampling methods besides a simple random sample, they were: stratified sample, the cluster sample, and the systematic sample. Below is an example that shows how the random number generator can be used to form those different types of samples.
Example
You are going to use the random number generator to generate different types of samples from the data.
This table displays six sets of quiz scores (each quiz counts 10 points) for an elementary statistics class.
| #1 | #2 | #3 | #4 | #5 | #6 |
|---|---|---|---|---|---|
| 5 | 7 | 10 | 9 | 8 | 3 |
| 10 | 5 | 9 | 8 | 7 | 6 |
| 9 | 10 | 8 | 6 | 7 | 9 |
| 9 | 10 | 10 | 9 | 8 | 9 |
| 7 | 8 | 9 | 5 | 7 | 4 |
| 9 | 9 | 9 | 10 | 8 | 7 |
| 7 | 7 | 10 | 9 | 8 | 8 |
| 8 | 8 | 9 | 10 | 8 | 8 |
| 9 | 7 | 8 | 7 | 7 | 8 |
| 8 | 8 | 10 | 9 | 8 | 7 |
Instructions: Use the Random Number Generator to pick samples.
- Create a stratified sample by column. Pick three quiz scores randomly from each column.
- Number each row one through ten.
- On your calculator, press Math and arrow over to PRB.
- For column 1, Press 5:randInt( and enter 1, 10). Press ENTER. Record the number. Press ENTER 2 more times (even the repeats). Record these numbers. Record the three quiz scores in column one that correspond to these three numbers.
- Repeat for columns two through six.
- These 18 quiz scores are a stratified sample.
- Create a cluster sample by picking two of the columns. Use the column numbers: one through six.
- Press MATH and arrow over to PRB.
- Press 5:randInt( and enter 1,6). Press ENTER. Record the number. Press ENTER and record that number.
- The two numbers are for two of the columns.
- The quiz scores (20 of them) in these 2 columns are the cluster sample.
- Create a simple random sample of 15 quiz scores.
- Use the numbering one through 60.
- Press MATH. Arrow over to PRB. Press 5:randInt( and enter 1, 60).
- Press ENTER 15 times and record the numbers.
- Record the quiz scores that correspond to these numbers.
- These 15 quiz scores are the systematic sample.
- Create a systematic sample of 12 quiz scores.
- Use the numbering one through 60.
- Press MATH. Arrow over to PRB. Press 5:randInt( and enter 1, 60).
- Press ENTER. Record the number and the first quiz score. From that number, count ten quiz scores and record that quiz score. Keep counting ten quiz scores and recording the quiz score until you have a sample of 12 quiz scores. You may wrap around (go back to the beginning).
Quick Tips for the Graphing Calculator
Because this is the first section that shows how to use the graphing calculator, there are also Quick Tips for using the graphing calculator toward the bottom of this page for reference. A few helpful tips for your graphing calculator:
- Adjust the contrast - Press
, then hold 
to increase the contrast or 
to decrease the contrast. - Capitalize letters and words - Press
to get one capital letter, or press , then to set all button presses to capital letters. You can return to the top-level button values by pressing again. - Correct a mistake - If you hit a wrong button, just hit
and start again. - Write in scientific notation - Numbers in scientific notation are expressed on the TI-83, 83+, 84, and 84+ using E notation, such that...
- 4.321 E 4 = \(\text{4}\text{.321}×{\text{10}}^{4}\)
- 4.321 E –4 = \(\text{4}\text{.321}×{\text{10}}^{–4}\)
Legend
represents a button press- [ ] represents yellow command or green letter behind a key
- < > represents items on the screen
Helpful Videos for the Graphing Calculator
Below are links to helpful videos for using the graphing calculator for the concepts covered on this page:
Additional Technology Tools
In addition to the graphing calculator, there are some additional technology tools that can be used for the concepts covered on this page. Below are links to helpful videos for those tools:
- Random Numbers and Sampling with Microsoft Excel:
Section Practice
None for this Section
