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: \(\displaystyle \operatorname{modes} (a)\) = --

1^st quartile (Q1): \(\displaystyle Q_{1}\) = --

3^rd 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: \(\displaystyle z = \frac{a_{1} - \overline{a}}{s}\) = --