Describing Data Numerically Using a Graphing Calculator: Study with Video Lessons, Practice Problems & Examples

To analyze larger datasets efficiently, utilize a TI-84 calculator to compute the five-number summary, which includes the mean, median, standard deviation, and first and third quartiles. Begin by entering your data into the calculator, then access the one-variable statistics function to retrieve essential statistics. The mean (x̄) represents the average, while the standard deviation (s_x) indicates variability. The quartiles provide insights into data distribution, with Q1 marking the 25th percentile and Q3 the 75th percentile, essential for understanding central tendency and variability in data analysis.

Find 5-Number Summary - TI-84 Calculator

Up until now, when we've calculated variables like the mean and standard deviation, all of that stuff has been done by hand. And while that's perfectly fine for smaller samples of, let's say, 5 or 6 numbers, and you need to know how to do that by hand, a lot of problems in this course will involve larger datasets of, let's say, 20 or 30 numbers. So doing this stuff by hand can get extremely time-consuming. I want to show you how we can use technology to make this a little bit easier. I'm going to show you how to get what's called a five-number summary on a TI-84 graphing calculator.

This five-number summary is going to have 5 important numbers that will help you answer all the questions on the variables and the distribution in the datasets. Alright? So again, if you have a TI-84 calculator, have it out because you're going to follow along with me. I'm going to have a list of steps for you to refer back to later, but the most important thing is that you're following along with me. So let's get started here.

We're going to jump right into our problem. We have the ages of students in a college statistics class that are listed in this table. We're going to use a calculator to find our mean, median, standard deviation, and first and third quartiles. That's five numbers, and it's going to be five numbers with their symbols right over here.

The first thing you're going to have to do here is get all your numbers into the calculator, and we've actually seen how to do this before. So we've got our calculators. I'm going to hit the stat button, and I'm going to go to the edit page. The edit page is going to basically bring up a table where I'm going to input some numbers. Now if you already have numbers here, I'm going to show you a way you can clear that out really quickly. Hit the stat button again, go to clear list, and then type in L1 that contains that list.

Hit the done key and then go back, and you should see that the page is blank now. So you can just edit you can put in all these numbers. So now we're just going to go ahead and plug all these numbers in one by one, sort of down the list. So I've entered 20, then 18, 21, 22, 20, 19, 31, 21, 24, 22, 19, 23, 18, 21, 21, 22, 20, 19, 27, and 20. If you've done this right, you should see L1 with a 21 there. That means you've entered 20 numbers, and that's the first step.

Now the second step is we're going to take that list, and you can go back, and basically just hit the second quit button to sort of get out of that screen. We're going to go to stats, and then you're going to go to the right, which is basically going to highlight the little calculator section. And you're going to go to 1-variable stats, which should be the very first entry.

So we're going to hit that button over here. It's going to ask you for which list do you want, and you're just going to plug in the list 1. You're just going to hit equals. Don't have to put anything for the frequency list, and then just hit calculate. Now what it spits out over here, is basically everything you need. This first window over here will tell you a lot of the stuff that's calculating either the mean or the standard deviation.

So what's x̄? It's actually the very, very first number on the screen, that's \(21.4\). That is the mean of the sample. For the standard deviation, your calculator doesn't know if the data is from a sample or a population. So it's going to display some extra info. There are two numbers over here that you need to look at. One is \(s_x\), and the other one is \(\sigma_x\). Remember, one's a sample, and one's a population. So basically, you're going to be looking at that \(s_x\) button for a sample. The standard deviation in this dataset is going to be \(3.1\), and I'm just going to keep it rounded to the nearest tenths place.

This tells us the number of data points, which is 20. And if we keep scrolling down, it'll give us some information about the distribution of values, the minimum, the maximum, the quartiles, and the medians. And that's what we need for the next couple of numbers. The first quartile is basically the cutoff where 25% of the data values are below that, and this is \(19.5\). The third quartile, where 75% of the data values are below that, is \(22\). The median gives \(21\).

So that's your five-number summary for the TI-84. Again, if you were asked about the mean, standard deviation, or variance, you'd be able to answer all of that with the information listed here. So that's it for this one, folks. Let me know if you have any questions, and I'll see you in the next one.

Find 5-Number Summary - TI-84 Calculator Example 1

Welcome back, everyone. Let's take a look at this example together. In this dataset, the data shows a sample of the monthly salaries in dollars of 30 employees at a medium-sized company. We're going to use a calculator to find a couple of important variables: the mean, the range, the standard deviation, and the variance. While this is not exactly the five-number summary that we saw in previous videos, we are actually going to use the steps to find those numbers in that readout because it's going to help us solve these numbers.

These are 4 very important variables that you'll often be asked to find in problems like these to help you kind of interpret the data. Now, again, this is a dataset of 30 numbers, and they're pretty big numbers. So doing this stuff by hand would be incredibly time-consuming. We'd be here until tomorrow.

So let's go ahead and use our calculators to make this a lot easier. Remember, the first step is we have to basically plug all this stuff into our calculator. So make sure you have your calculator out, and let's go ahead and start doing that. The first thing we have to do, remember, is go to the stat menu, and we have to go to the edit button so we can basically get this sort of screen where we can type in all the numbers.

And the rest of this is basically just plugging in all of these numbers. So if you've already done this step, you can go ahead and just skip the rest of this. Let's go ahead and type in these numbers. We've got 41, 4174, 4507, 1860, 2294, 2130, 2095, 4772, 4092. Whoops, that's supposed to be a 9, 4092. Then we got 2638, 3169, 1466, 2238, 1330, 2482, 3135. Halfway done.

4444, 4171, 3919, 4735, 1130, 2685, 4380, 1769, 3391. Almost done. 2515, 4485, 3853, 3433. Whoops, that's supposed to be a 33. And then I've got 2215, and the last one is 1955. That took a long time. But, after you plug in all these numbers, remember, that's the 30th entry, so I know I have 30 numbers in here. Now what we do is we move on to the second step.

You've already plugged this stuff into your calculators. The second step is we hit the stat button, and we have to go into the calculator menu. So that's the stat button. We just go over to the right, and we click 1 variable stats. So we hit the enter key, and we're just gonna use that same list that we just populated, and then we're going to go ahead and hit the calculate button. Frequency list, you can just leave as empty, and then hit that calculator button. That's the second and third steps.

Now, you've got this readout, and we're basically just going to go ahead and find the numbers that we're looking for. Let's take a look at the first one, the mean. Remember, for the mean, that's just x bar. In this case, x bar is actually the first number, which is 3048. Remember these types of problems when you're given integers, you should always basically round to the first decimal place, one more decimal place than you have. So I have x bar is equal to 3048.7.

Now let's look at the second number, the range. If you look through your calculator screen, if you sort of scroll down in this menu, you can see that there's no number that actually tells us what the range is. So how do we find that? Well, the range, think back to what the range actually means. The range is equal to the max minus the min. It won't tell us what the range is. We just have to find it out by using these numbers. So this is going to be 4772 minus 1130. If you go ahead and work this out in a calculator, you should see that this is 3642. So the range here is 3642.

Let's move on to the next one, the standard deviation. Remember, standard deviation is S because we're talking about a sample here. Otherwise, we would use sigma, lowercase sigma. So this is really just going to be S. And in a calculator, remember that the calculator spits this out as Sx. Scroll back on your screen, and you should see Sx, which is that fourth number. It tells us 1129.5. We always just round up to that decimal place. So this is going to be 1129.5.

The last thing we have to find is variance. Remember the relationship between variance and standard deviation is that the variance is the standard deviation squared. In this case, the variance is going to be S squared. It won't tell us this number automatically from this window, but we can calculate this if we just square this number. If you go ahead and actually do that, what we find is that this is equal to 1275761. That's just rounded to the nearest ones place. So that is the variance of this dataset. These are your four numbers: the mean, the range, the standard deviation, and the variance.

We found all of this using a calculator. Yes, it was a little bit tedious to plug all the numbers in, but it beats having to do this stuff by hand. That's it for this one, folks. Thanks for watching, and I'll see you in the next one.

Here’s what students ask on this topic:

How do you enter data into a TI-84 calculator for a five-number summary?

To enter data into a TI-84 calculator for a five-number summary, follow these steps: First, press the 'STAT' button and select '1: Edit' to access the data entry screen. If there are existing numbers, clear them by pressing 'STAT', selecting '4: ClrList', and entering 'L1'. Then, return to the 'Edit' screen. Enter your data points one by one into list L1. Once all data points are entered, you can proceed to calculate the five-number summary.

What is the five-number summary on a TI-84 calculator?

The five-number summary on a TI-84 calculator includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value. These statistics provide a quick overview of the data distribution, showing the range, central tendency, and variability. To calculate it, enter your data, then use the '1-Var Stats' function to retrieve these values.

How do you calculate the mean and standard deviation using a TI-84 calculator?

To calculate the mean and standard deviation using a TI-84 calculator, first enter your data into list L1. Then, press 'STAT', navigate to 'CALC', and select '1: 1-Var Stats'. Enter 'L1' and press 'ENTER'. The calculator will display the mean (x̄) and standard deviation (sx for sample, σx for population). The mean is the average of the data, and the standard deviation measures the data's variability.

What do Q1 and Q3 represent in a five-number summary?

In a five-number summary, Q1 (the first quartile) represents the 25th percentile, meaning 25% of the data points are below this value. Q3 (the third quartile) represents the 75th percentile, meaning 75% of the data points are below this value. These quartiles help in understanding the spread and distribution of the data, indicating where the middle 50% of the data lies.

How do you interpret the output of the '1-Var Stats' function on a TI-84 calculator?

The '1-Var Stats' function on a TI-84 calculator provides several key statistics: the mean (x̄), standard deviation (sx for sample, σx for population), the number of data points (n), the minimum value, Q1, median, Q3, and the maximum value. The mean indicates the average, the standard deviation shows variability, and the quartiles (Q1 and Q3) help understand the data distribution. The minimum and maximum values show the range of the dataset.