Descriptive Statistics Calculators

I greet you this day,
These calculators are for vertical entries of data only
To use the calculators for horizontal data entries, please visit Descriptive Statistics Calculators (Vertical data entries only)
I wrote the codes for the calculators using JavaScript, a client-side scripting language.
Comments, questions, and constructive criticisms are welcome. You may contact me.
Thank you for visiting.
Samuel Dominic Chukwuemeka (SamDom For Peace)
B.Eng., A.A.T, M.Ed., M.S

Measures of Center

Case 1
Given: Raw Dataset, $X$
Sort the Data
To Calculate: Mean, Median, Mode, Midrange
Show all steps

Raw Data

Sorted Data (Ascending Order)

$\Sigma x$ =

$n$ =

$\bar{x}$ =

$\tilde{x}$ =

$\widehat{x}$ =
(If the dataset is multimodal or has no mode, click inside and scroll all the way to the end as applicable)

$min$ =

$max$ =

$x_{MR}$ =

Case 2
Given: Ungrouped Dataset and Frequency
To Calculate: Mean
Show all steps

Ungrouped Data, $X$

Frequency, $f$

$f * x$

$\Sigma fx$ =

$\Sigma f$ =

$\bar{x}$ =

Case 3
Given: Grouped Dataset (Lower Class Limit and Upper Class Limit) and Frequency
To Calculate: Mean
Show all steps

Lower Class Limit, $LCL$

Upper Class Limit, $UCL$

Frequency, $f$

$x_{mid}$

$f * x_{mid}$

$\Sigma fx_{mid}$ =

$\Sigma f$ =

$\bar{x}$ =

Case 4
Given: Grouped Dataset (Lower Class Limit and Upper Class Limit), Frequency, and Assumed Mean
To Calculate: Mean
Show all steps

Lower Class Limit. $LCL$

Upper Class Limit, $UCL$

Frequency, $f$

Assumed Mean =

$x_{mid}$

$D = x_{mid} - AM$

$f * D$

$\Sigma fD$ =

$\Sigma f$ =

$\bar{x}$ =

Case 5
Given: Raw Dataset, Trim Percent
Sort the Data
To Calculate: Trimmed Mean
Show all steps

Raw Data, $X$

Trim % from the data

Sorted Data (Ascending Order)

This implies that value(s) is/are trimmed from each end of the sorted data

Trimmed Data

Sum of Trimmed Data =

Sample Size of Trimmed Data =

Trimmed Mean =

Case 6
Given: Assumed Mean, Deviations from the Assumed Mean
To Calculate: Mean
Find the Dataset
Sort the Dataset
To Calculate: Median, Mode, Midrange
Show all steps

Assumed Mean =

$x - AM$

$\Sigma D$ =

$n$ =

$\bar{x}$ =

Raw Data, $X$

Sorted Data

$\tilde{x}$ =

$\widehat{x}$ =
(If the dataset is multimodal or has no mode, click inside and scroll all the way to the end as applicable)

$min$ =

$max$ =

$x_{MR}$ =

Case 7
Given: Raw Dataset
To Calculate: Geometric Mean
Show all steps

Raw Data, $X$

$\Pi x$ =

$n$ =

GM =

Measures of Spread

Case 1 (First Method)
Given: Raw Dataset
Sort the Data
To Calculate: Range, Variance, Standard Deviation, Coefficient of Variation, Mean Deviation
Show all steps

Raw Data, $X$

Sorted Data (Ascending Order)

$min$ =

$max$ =

$range$ =

$\Sigma x$ =

$n$ =

$\bar{x}$ =

$x - \bar{x}$

$(x - \bar{x})^2$

$\Sigma (x - \bar{x})^2$ =

$n - 1$ =

$s^2$ =

$s$ =

$CV$ = %

$|x - \bar{x}|$

$\Sigma |x - \bar{x}|$ =

$MAD$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

$CV$ = %

Case 2 (First Method)
Given: Ungrouped Dataset and Frequency
To Calculate: Variance, Standard Deviation, Coefficient of Variation, Mean Deviation
Show all steps

Ungrouped Data, $X$

Frequency, $f$

$f * x$

$\Sigma fx$ =

$\Sigma f$ =

$\bar{x}$ =

$x - \bar{x}$

$(x - \bar{x})^2$

$f(x - \bar{x})^2$

$\Sigma f(x - \bar{x})^2$ =

$\Sigma f - 1$ =

$s^2$ =

$s$ =

$CV$ = %

$|x - \bar{x}|$

$f|x - \bar{x}|$

$\Sigma f|x - \bar{x}|$ =

$MAD$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

$CV$ = %

Case 3 (First Method)
Given: Grouped Dataset (Lower Class Limit and Upper Class Limit) and Frequency
To Calculate: Variance, Standard Deviation, Coefficient of Variation, Mean Deviation
Show all steps

Lower Class Limit, $LCL$

Upper Class Limit, $UCL$

Frequency, $f$

$x_{mid}$

$fx_{mid}$

$\Sigma fx_{mid}$ =

$\Sigma f$ =

$\bar{x}$ =

$x_{mid} - \bar{x}$

$(x_{mid} - \bar{x})^2$

$f(x_{mid} - \bar{x})^2$

$\Sigma f(x_{mid} - \bar{x})^2$ =

$\Sigma f - 1$ =

$s^2$ =

$s$ =

$CV$ = %

$|x_{mid} - \bar{x}|$

$f|x_{mid} - \bar{x}|$

$\Sigma f|x_{mid} - \bar{x}|$ =

$MAD$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

$CV$ = %

Case 1 (Second Method)
Given: Raw Dataset
Sort the Data
To Calculate: Range, Variance, Standard Deviation, Coefficient of Variation
Show all steps

Raw Data, $X$

Sorted Data (Ascending Order)

$min$ =

$max$ =

$range$ =

$x^2$

$\Sigma x^2$ =

$n$ =

$n(\Sigma x^2)$ =

$\Sigma x$ =

$(\Sigma x)^2$ =

$n(\Sigma x^2) - (\Sigma x)^2$ =

$n - 1$ =

$n(n - 1)$ =

$s^2$ =

$s$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

Case 2 (Second Method)
Given: Ungrouped Dataset and Frequency
To Calculate: Variance, Standard Deviation
Show all steps

Ungrouped Data, $X$

Frequency, $f$

$fx$

$x^2$

$fx^2$

$\Sigma fx^2$ =

$\Sigma f$ =

$\Sigma f(\Sigma fx^2)$ =

$\Sigma fx$ =

$(\Sigma fx)^2$ =

$\Sigma f(\Sigma fx^2) - (\Sigma fx)^2$ =

$\Sigma f - 1$ =

$\Sigma f(\Sigma f - 1)$ =

$s^2$ =

$s$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

Case 3 (Second Method)
Given: Grouped Dataset (Lower Class Limit and Upper Class Limit) and Frequency
To Calculate: Variance, Standard Deviation
Show all steps

Lower Class Limit, $LCL$

Upper Class Limit, $UCL$

Frequency, $f$

$x_{mid}$

$fx_{mid}$

$x_{mid}^2$

$fx_{mid}^2$

$\Sigma f(x_{mid}^2)$ =

$\Sigma f$ =

$\Sigma f(\Sigma fx_{mid}^2)$ =

$\Sigma fx_{mid}$ =

$(\Sigma fx_{mid})^2$ =

$\Sigma f(\Sigma fx_{mid}^2) - (\Sigma fx_{mid})^2$ =

$\Sigma f - 1$ =

$\Sigma f(\Sigma f - 1)$ =

$s^2$ =

$s$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

Range Rule of Thumb

Case 6
Given: Assumed Mean, Deviations from the Assumed Mean
To Calculate: Variance, Standard Deviation, Coefficient of Variation
Find the Dataset
Sort the Dataset
To Calculate: Range
Show all steps

Assumed Mean =

$x - AM$

$\Sigma (x - AM)$ =

$n$ =

$\bar{x}$ =

$n - 1$ =

$s^2$ =

$s$ =

$CV$ = %

Raw Data, $X$

Sorted Data

$min$ =

$max$ =

$range$ =

................................................................
Population
................................................................

$N$ =

$\sigma^2$ =

$\sigma$ =

$CV$ = %

Measures of Position

Case 1
Given: Raw Dataset
Sort the Data
To Calculate: Five- Number Summary of Dataset, Interquartile Range, Semi-interquartile Range, Midquartile, Lower Fence, Upper Fence, Outliers

Raw Data, $X$

Sorted Data (Ascending Order)

$n$ =

$min$ =

$Q_1$ =

$Q_2$ =

$Q_3$ =

$max$ =

$IQR$ =

$SIQR$ =

$MQ$ =

$LF$ =

$UF$ =

Outliers =

Percentiles (Convert a Data Value to a Percentile)

Case 2
Given: Raw Dataset
Sort the Data
To Calculate: Percentile of a Data Value
Show all steps

Raw Data

Calculate the percentile of

Sorted Data (Ascending Order)

The data values less than are:

The count of those values is:

Sample Size =

Answer is th percentile

Percentiles (Convert a Percentile to a Data Value)

Case 3
Given: Raw Dataset
Sort the Data
To Calculate: the nth Percentile
Show all steps

Raw Data

Calculate the th percentile

Sorted Data (Ascending Order)

Sample Size =

Position =
If it is not an integer, round up to the next integer and read the value
If it is an integer, read the values at this position and next position, and find the mean.

Value at Position =

Next Position =

Value at Next Position =

Answer is

Case 4
Given: Variable, Mean, Standard Deviation
To Calculate: Standard Score; tell whether a data value is usual or unusual

Data Value =

Mean =

Standard Deviation =

The difference between the data value and the mean =

The difference is standard deviations

Standard Score =