5-Number Summary Using a TI-84: Videos & Practice Problems

To analyze larger datasets efficiently, use a TI-84 calculator to compute a 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. The mean (x̄) and standard deviation (s) can be found alongside the quartiles, providing a comprehensive overview of the data distribution. This method streamlines calculations, making it easier to interpret statistical results from larger samples.

Find 5-Number Summary - TI-84 Calculator

So up until now, when we've calculated variables like the mean and standard deviation, all of that has been done by hand. While that's perfectly fine for smaller samples of, let's say, five or six 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. Doing this 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 five important numbers that will help you answer all the questions about the variables and the distribution in the datasets. 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 that'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, as we've actually seen how to do this before. 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 will bring up a table like this where I'm going to input some numbers. Now if you already have numbers in here, I'm going to show you where you can clear that out really quickly. Hit the stat button again, go to clear list, and then type in that list that contains that list.

Hit the done key, and then go back, and you should see that the page is blank now. You can just put in all those numbers. So now we're just going to go ahead and plug all these numbers in one by one, down the list. So I've got 20, then I've got eighteen, twenty-one, twenty-two, 20, nineteen, thirty-one, twenty-one, twenty-four, twenty-two, 19, twenty-three, 18, twenty-one, twenty-one, twenty-two, 20, 19, twenty-seven, and 20. If you've done this right, you should see list one 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 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 over here to the right, which is basically going to highlight the little calculator section. You're going to go to one-variable stats, which should be the very first entry. So one var stats.

Okay? 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 list one. You're just going to hit equals. You don't have to put anything for the frequency list, and then just hit calculate.

Now what it spits out over you with what it spits out on the screen is basically everything you need here. Now it's going to spit out a lot of information, some of which you don't need. But basically, this first window over here will show you a lot of the stuff that's calculating either the mean or the standard deviation.

So what's \( \bar{x} \)? It's actually the very, very first number on the screen, that 21.4. So that's 21.4. That is the mean of the sample. What about the standard deviation? Well, basically, what happens here is that 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, one's a population. So basically, what you can always assume here is that if you're looking at a sample, you're going to be looking at that \(s_x \). So 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.

It tells us the number of data points, which is 20. If we keep scrolling down over here, 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. So it gives us the minimum and maximum values. We don't need that stuff. We need the first and third quartiles. The first quartile is basically the cutoff where 25% of the data values are below that.

This is 19.5, like this. Then the third quartile, which is where 75% of the data values are below that. So in other words, this is 22. And then the median over here gives us 21. So that's your five-number summary for TI-84. Again, if you were asked about the mean or the standard deviation or the variance, you'd be able to answer all of that with the information that you have listed here.

So that is the second and third steps. You're just going to go to one var stats, plug in that list, and you're just going to hit the calculator, and it's going to show you everything. Alright? 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 following 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. So 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 four 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 till 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 to 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. So let's go ahead and type in these numbers. We've got 4141, 4174, 4507, 1860, 2294, 2130, 2095, 4772, 4092, 2638, 3169, 1466, 2238, 1330, 2482, 3135, 4440, 4171, 3919, 4735, 1130, 2685, 4380, 1769, 3391, 2515, 4485, 3853, 3433, and the last one is 1955.

That took a long time. But basically, after you plug in all these numbers, remember, that's the thirtieth entry, so I know I have 30 numbers in here. Now what we do is we move on to the second step. So 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 go over to the right, and we click on one variable stats. So we hit the enter key, and we're just going to use that same list that we just populated, and then we're just going to go ahead and hit the calculate button.

Frequency list, you can just leave as empty, and then hit that calculator button, and that's the second and third steps. So 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. That's the mean. Remember, for the mean, it's just x bar. So in this case, what we see from our readout, x bar is actually the first number, which is 3048.7. Remember, in these types of problems, when you're given integers, you should always just round to the first decimal place, one more decimal place than you have. So let me write this a little bit bigger.

Now let's look at the second number that we need, which is the range. If you look through your calculator screen, 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—it is equal to the max minus the min. So it's the max minus the min. So it won't tell us what the range is. We just have to go find it out by using these numbers.

So this is going to be $4772 minus $1130. And if you go ahead and work this out in a calculator, what you should see is that this is $3642.

So the range here is 3642. Let's move on to the next one, the standard deviation. Remember, the 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 on a calculator, it spits this out as sx. Scroll back in your screen, and you should see sx, which is that fourth number. It tells us 1129.5. Remember, we always round up to that decimal place.

The last thing we have to find is variance. Remember, the relationship between variance and standard deviation is that variance is the standard deviation squared. So in this case, the variance is s2. So we calculate this by squaring the number and find it is approximately 1275761, to the nearest ones place. That is the variance of these datasets. So these are your four numbers.

We've got the mean, the range, the standard deviation, and the variance. We found all of this using a calculator. Yes, it was a 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 I 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, first press the 'STAT' button and select '1:Edit'. This will open a table where you can input your data. If there are existing numbers, clear them by pressing 'STAT', selecting '4:ClrList', and entering 'L1'. Once the list is cleared, return to the 'Edit' screen and input your data values one by one into 'L1'. Ensure all data points are entered correctly before proceeding to the next steps for statistical analysis.

What steps are involved in calculating a five-number summary using a TI-84 calculator?

To calculate a five-number summary using a TI-84 calculator, first enter your data into the calculator. Then, press 'STAT', navigate to 'CALC', and select '1-Var Stats'. Enter 'L1' for the list and press 'ENTER'. The calculator will display the mean (x̄), standard deviation (s), and other statistics. Scroll down to find the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. These five numbers form the five-number summary, providing insights into the data's distribution and variability.

What is the significance of the first and third quartiles in a five-number summary?

The first quartile (Q1) and third quartile (Q3) in a five-number summary are crucial for understanding data distribution. Q1 represents the value below which 25% of the data falls, indicating the lower quartile. Q3 represents the value below which 75% of the data falls, indicating the upper quartile. These quartiles help identify the spread and skewness of the data, providing insights into variability and potential outliers. Understanding Q1 and Q3 is essential for making informed decisions based on statistical properties.

How does a TI-84 calculator differentiate between sample and population standard deviation?

A TI-84 calculator displays two standard deviation values: 'Sx' for sample standard deviation and 'σx' for population standard deviation. When analyzing a sample, use 'Sx', which accounts for sample variability. For a population, use 'σx', which assumes the data represents the entire population. The calculator does not automatically determine whether the data is a sample or population, so it's important to select the appropriate standard deviation based on your dataset's context.

What information does the one-variable statistics function provide on a TI-84 calculator?

The one-variable statistics function on a TI-84 calculator provides comprehensive data analysis. It calculates the mean (x̄), standard deviation (Sx for sample, σx for population), and the number of data points. Additionally, it offers a five-number summary, including the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. This function is essential for understanding data distribution, variability, and central tendency, aiding in statistical analysis and decision-making.