# List Analyzer

A tool to analyze a tuple (finite, ordered list of elements) and give values commonly asked for in AP® Statistics problems. The formulas and terminology used change based on input. NaN means Not a Number.

$$\displaystyle a$$ represents  .

## Input

Assume that $$\displaystyle a$$ is a 10-tuple ($$\displaystyle N = 10$$) that represents a sample of the population of interest.

Reordered tuple (will be used for all further calculations):

$$\displaystyle a = ()$$

## Tuple information

Number of elements: $$\displaystyle N$$ = --
Sum of all elements: $$\displaystyle S_{a} = \sum a_{i}$$ = --
Mean (average value): $$\displaystyle \overline{a} = \frac{\sum a_{i}}{N}$$ = --
Sample standard deviation: $$\displaystyle s = \sqrt{\frac{\sum (a_{i} - \overline{a})^{2}}{N - 1}}$$ = --
Sample variance: $$\displaystyle s^{2}$$ = --
Standard error of the mean (estimator): $$\displaystyle \widehat{\sigma}_{\overline{a}} = \frac{s}{\sqrt{N}}$$ = --
Minimum: $$\displaystyle a_{1}$$ = --
Median: $$\displaystyle a_{1}$$ = --
Maximum: $$\displaystyle a_{1}$$ = --
Modes: $$\displaystyle \operatorname{modes} (a)$$ = --
1st quartile (Q1): $$\displaystyle Q_{1}$$ = --
3rd quartile (Q3): $$\displaystyle Q_{3}$$ = --
Interquartile Range (IQR): $$\displaystyle \mathrm{IQR} = Q_{3} - Q_{1}$$ = --
Five-number summary (min, Q1, median, Q3, max): $$\displaystyle \operatorname{fiveNumSummary} (a)$$ = --
1.5 ⋅ IQR: $$\displaystyle 1.5 \cdot \mathrm{IQR}$$ = --
Non-outlier minimum (1.5 ⋅ IQR rule): $$\displaystyle Q_{1} - (1.5 \cdot \mathrm{IQR})$$ = --
Non-outlier maximum (1.5 ⋅ IQR rule): $$\displaystyle Q_{3} + (1.5 \cdot \mathrm{IQR})$$ = --
Outliers (1.5 ⋅ IQR rule): $$\displaystyle \operatorname{outliers} (a)$$ = --

## Element information

Current element: $$\displaystyle a_{1} =$$ --
Frequency (amount): $$\displaystyle f_{a}$$ = --
Frequency (relative): $$\displaystyle f_{r} = \frac{f_{a}}{N}$$ = --
Cumulative relative frequency (percentile): $$\displaystyle \sum_{i = 1}^{1} f_{r}$$ = -- (--th percentile, --th percentile from the end)
Relative error (treating mean value as expected): $$\displaystyle \eta = \left|\frac{a_{1} - \overline{a}}{\overline{a}}\right|$$ = -- (--%)
Difference from mean: $$(a_{1} - \overline{a})$$ = --
z-score: $$\displaystyle z = \frac{a_{1} - \overline{a}}{s}$$ = --