Visualising and analysing statistics with the fx-CG100

From investigating real-world data to visualising probability distributions, the fx-CG100 is a powerful tool for tackling statistics in A-level maths.

As we explore in this blog, the calculator’s dedicated Statistics and Distribution apps offer various ways for students to link numbers and calculations with visual analysis and hypotheses.

Exploring data with the Statistics app

The fx-CG100’s Statistics app offers all sorts of ways to explore real data with your students and connect the numbers to topics like correlation, regression and summary statistics.

When you open the app, you’re presented with up to 26 lists that can be populated with data.

You can then carry out tasks such as filling List 1 and List 2 with values, generating a scatter plot from the ‎two-variable statistical data and drawing a regression graph on top of it.

Once the scatter plot and regression line are displayed, students can explore how closely the data points cluster around the line and discuss what that tells them about the strength and direction of correlation.

The trace function (accessible via Tools) makes it easy to identify specific coordinate pairs and explore which points are outliers or have a disproportionate effect on the trend. This visual approach helps students connect the numerical correlation they’ve calculated with what it actually means in context.

Another key advantage of the Statistics app is the capability to calculate summary statistics from one or two-variable data. This can prove particularly useful for students when they’re answering exam questions and need to provide essential values such as:

• Mean, mode and median
• Sum of the list values
• Sum of squares
• Population standard deviation
• Sample standard deviation

Unpacking binomial probabilities with Distribution

Teachers have told us that the Distribution app is an effective and highly popular tool among A-level maths students, partly thanks to its strong visual element.

In response to the positive feedback to this feature, we’ve given it pride of place in the fx-CG100’s menu. It now sits between Equation and Statistics on the home screen and can be accessed via the shortcut 3.

Let’s look at a specific example of how to use Distribution to unpack binomial probability problems. We’ll use a question that asks for the probability that X = 6, when the number of trials is 10 and the probability of success is 0.6.

When you open the app, you’ll be presented with distribution options including binomial, normal, Poisson and geometric. For this question, we’ll select binomial, which will open the Setup tab.

Here you’ll see the following fields:

• Tail – Choose from four available regions: left, centre, right and exact. For this question, we need to choose exact.
• Data – Select between variable, which is the default option, or list, which will use a list of x values to create a table of probabilities.
• X – Enter the X value you want to find (6 in this example).
• Numtrial – Confirm the number of trials specified in the question (10).
• P – Add the probability of success (0.6)
• Colour – Set the colour of the displayed graph.

When you’ve entered the parameters, press the right tab key to see the results. This will display a screen showing the calculated probability (in this case, 0.2508), as well as a graph of the distribution.

Diving deeper into the distribution

The Distribution app provides a graphical representation that you can explore and analyse with your students to get further insights into probabilities.

In this example, once the distribution has been graphed, you can play around with different values within the same region. If 6 is still highlighted on the X scale, you can plug in different variables to find their respective probabilities.

Entering 4, for example, will show that the probability of having four successes from ten independent trials, when the chance of success is 0.6, is 0.1115, or 11.15%.

To mix things up even more, you can press Tools, which opens a window providing options to view and edit values, adjust the view window or change the tail.

Leaving 4 as the highlighted variable but selecting a right-hand tail, for instance, will produce a new graph and results showing that P (X ≥ 4) for X ̴   B (10, 0.6) = 0.9452.

Handling hypothesis tests

The strong element of visualisation incorporated into the Distribution app can also come in useful when exploring hypothesis testing with your students.

Let’s look at exactly what the app can do, this time using the following example question based on a normal distribution: find P (175 ≤ X ≤ 185) for X ̴   N (174, 49).

When these parameters have been added to the relevant fields and graphed, you’ll see the normal distribution’s standard bell curve and a result at the top of the screen showing that P = 0.3852.

If you’re investigating two-tailed hypothesis tests with an A-level class, you might want to look for a symmetrical range of values within this distribution. You can do this simply by adjusting the probability.

To find the 95% symmetrical values for X ̴   N (174, 49), for instance, scroll across to highlight the probability value on the Results tab and enter the percentile range as a decimal value (0.95).

You’ll then see new X values and a shaded section of the graph showing that the bounds for the required range are 160.28 and 187.71. It’s important to remember these values are truncated, so students should get into the habit of displaying them in full (using Tools > View Value) to ensure accurate rounding.

Whatever stage you’re at with the fx-CG100, we offer resources to help you maximise the benefits of the calculator.

If you’re just getting started, you can sign up for free introductory training. To dive deeper into specific functionality and applications, take a look at some of our specialist resources and how-to videos