1 List Focused Calculators Plotting and Other Keys Examples

This page contains examples for the "sum stats", "nrmProb", "hist(b)", "box", "box(n)", "prcntl(x)" and "prcntl⁻¹(x)" keys from the 1 List Statistics, Normal Distribution and Student's-t Distribution Focused Calculators.

Sample Data

This text area contains the data for these examples.

29.6, 58.5, 40.0, 59.4, 49.2, 53.6, 51.8, 43.7, 50.3, 54.5, 46.2, 36.5, 57.8, 54.4, 60.4, 55.5, 46.8, 42.2, 46.2, 52.1, 53.0, 61.7, 20.2, 46.4, 45.5, 38.9, 50.1, 42.3, 57.9, 59.4

The data can be copied and pasted in to list x using the List Manager.

"sum stats" key

Pressing shift "sum stats" will write the summary statistics to a History details item.
Pressing the "(i)" (letter i in a circle) button on the toolbar will display the most recent history detail:

sum stats - Calculates summary statistics of list x.
        48.8033 : mean
       1,464.10 : sum
       74,069.3 : sumSq
        9.49833 : stdev
        9.33868 : stdevp
        30.0000 : n
        20.2000 : min
        44.1500 : Q1
        50.2000 : median
        55.2500 : Q3
        61.7000 : max

Note that the History Details will use the current number format settings in Options.
For this example the number format is set to 6 significant digits.

Generate a normal probability plot using the "nrmPrb" key

Pressing the "nrmPrb" key will display a normal probability plot of the sample data.
This key is not on the 1 List Statistics Calculator.

Generate a 3 bin histogram using the "hist(b)" key

Entering 3, then pressing the "hist(b)" key will display a 3 bin histogram of the sample data.

Generate a box plot using the "box" key

Pressing the (shift) "box" key will display a box plot of the sample data.

The box plot is as described for Fig 3 of the Wikipedia reference:

The box is drawn from Q1 to Q3 with a horizontal (double thickness) line drawn in the middle to denote the median.
From above the upper quartile, a distance of 1.5 times the IQR is measured out and a whisker is drawn up to the largest observed point from the dataset that falls within this distance. Similarly, a distance of 1.5 times the IQR is measured out below the lower quartile and a whisker is drawn up to the lower observed point from the dataset that falls within this distance. All other observed points are plotted as outliers.

Calculate the percentile and inverse using the "prcntl(x)" and "prcntl⁻¹(x)" keys.

Using the sample data, calculate the 0.25 percentile:

Value	Keystrokes	Display	Description
0.25	shift prcntl(x)	44.2	Calculates the 0.25 (Q1) percentile.

This key is compatable with the percentile function found in spreadsheets, or second variant in the Wikipedia reference.

Using the sample data, calculate the percentile for the value of 55:

Value	Keystrokes	Display	Description
55	shift prcntl⁻¹(x)	0.741	Calculates the percentile for the value.

Calculate the standard score the "std(x)" key.

This key is not on the 1 List Statistics Calculator.

Using the sample data, calculate the standard score of 55:

Value	Keystrokes	Display	Description
55	shift "std(x)"	0.652	Calculates the standard score.

Use the "r norm" key to generate a list of normally distributed numbers.

The "r norm" key will use the values stored in x̄, s and n to generate a list of numbers in list x.
This key is not on the 1 List Statistics Calculator.

Generate 300 numbers with a mean of 100 and a standard deviation of 7.

Value	Keystrokes	Display	Description
100	x̄	100	Stores the mean.
7	s	7.00	Stores the standard deviation.
300	n	300	Stores n.
	shift "r norm"	300	Generates the values.

The x̄ and s keys can be used to calculate the actual values for this random sample.

Use the "box(n)" key to generate multiple box plots.

The "box(n)" key will plot up to 5 box plots for data in lists a-e.

Use the "r norm" key to generate 5 lists with different standard deviations and compare the box plots.

Value	Keystrokes	Display	Description
100	x̄	100	Stores the target mean.
2	s	2.00	Stores the target standard deviation.
200	n	200	Stores n.
	shift "r norm"		Generates the values.
	STO lista		Stores the values to list a.
5	s	5.00	Stores the standard deviation.
	shift "r norm"		Generates the values.
	STO listb		Stores the values to list b.
10	s	10.0	Stores the standard deviation.
	shift "r norm"		Generates the values.
	STO listc		Stores the values to list c.
15	s	15.00	Stores the standard deviation.
	shift "r norm"		Generates the values.
	STO listd		Stores the values to list d.
20	s	20.0	Stores the standard deviation.
	shift "r norm"		Generates the values.
	STO liste		Stores the values to list e.
5	shift box(n)		Displays the box plots.