Statistics and probability in Scientific calculator plus 991 for Android

Statistics on the calculator starts from one question: do you have the data, or only the model? With the data in hand, STAT mode summarises it or fits a curve to it. With a model instead, such as a mean and a standard deviation or a number of trials and a chance of success, the distribution menu gives the probability directly. This page says which tool fits which job, and where each is covered.

Which page for which job

Two tools

STAT mode works on data. Press MODE and choose STAT/DISTR, then press SHIFT 1 STAT and choose a calculation type on the DATA tab. The statistics editor opens: a table with one column for single-variable data, or an x and a y column for paired data, and a Frequency column beside them for values that repeat. From the numbers in it the mode works out every statistic at once, or fits a model and reports how well it fits.

The distribution menu works on a model. Press SHIFT 3 DISTR. Each of its sixteen functions is an ordinary function: choose normalcdf, say, give it the bounds, the mean and the standard deviation, and press =. No data is involved, and the answer is a probability or a value, like any other calculation. The menu is not tied to STAT mode: it opens in the ordinary calculation mode as well.

The two come closest in one place. The Distribution tab of the STAT menu has →t, which turns a value from the entered data into a standard score, and P, Q and R, which give areas under the standard normal curve.

The STAT menu

In STAT mode every statistic of your data comes from one menu, SHIFT 1 STAT, laid out as tabs. It reopens on whichever tab you used last.

• DATA opens the editor, runs a calculation, and lists the calculation types, with a tick beside the one in use.
• Edit inserts and deletes rows. It is there only while the editor is open.
• Summation holds ∑x, ∑x², ∑x³ and ∑x⁴, and for paired data ∑y, ∑y², ∑xy and ∑x²y.
• Variable holds the means, the variances, the standard deviations and the count n.
• Min/Max holds min(x), Q1, Med, Q3 and max(x), and for paired data min(y) and max(y).
• Distribution holds P(t), Q(t), R(t) and →t.
• Regression holds the fitted coefficients, r (the correlation coefficient), the estimates x̂ and ŷ read off the fitted model, and the fitted equation. It is there only for paired data; the quadratic type has c, R², x̂1 and x̂2 as well.

The menu works only in STAT mode. Anywhere else, the same keys show the message Supported only in STAT mode.

Eight calculation types

The types are listed on the DATA tab of SHIFT 1 STAT, with a tick beside the one in use. One is for a single column of data; the other seven fit a model to paired data.

Choosing a type opens the editor for it. Single-variable data and paired data are kept apart, so switching between the two loses neither; switching from one regression type to another keeps the same x and y columns and simply refits them.

What is kept, and how results show

• The data outlives the mode: it survives leaving STAT and is saved when the app closes.
• Statistics are shown to up to eleven decimal places.
• Every statistic is also a variable. Chosen from its tab, it goes into the calculation you are typing, so x̄ or sx can be used in a longer expression.
• A statistic that cannot be worked out is shown as Indeterminate rather than raising an error. A single value (n = 1) does this to the sample variance and standard deviation, s²x and sx, which divide by n − 1.

Decimals for probabilities

At a glance