If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

Let everything that has breath praise the LORD! Praise the LORD. - Psalm 150:6

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka # 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)

(If the dataset is multimodal or has no mode, click inside and scroll all the way to the end as applicable)

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

Ungrouped Data, $X$
Frequency, $f$

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, $f$

 $x_{mid}$ $f * x_{mid}$

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, $f$

 $x_{mid}$ $D = x_{mid} - AM$ $f * D$

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

Raw Data, $X$

% from the data

Sorted Data
(Ascending Order)

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

 Trimmed Data

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

$x - AM$

 Raw Data, $X$ Sorted Data

(If the dataset is multimodal or has no mode, click inside and scroll all the way to the end as applicable)

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

Raw Data, $X$

## 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)

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

%

 $|x - \bar{x}|$

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

%

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, $f$

 $f * x$

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

%

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

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

%

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, $f$

 $x_{mid}$ $fx_{mid}$

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

%

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

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

%

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)

 $x^2$

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

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

Ungrouped Data, $X$
Frequency, $f$

 $fx$ $x^2$ $fx^2$

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

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, $f$

 $x_{mid}$ $fx_{mid}$ $x_{mid}^2$ $fx_{mid}^2$

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

### Range Rule of Thumb

Case 4
Given: Minimum, Maximum
To Calculate: Range, Standard Deviation (estimated)

Case 5
Given: Range
To Calculate: Standard Deviation (estimated)

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

$x - AM$

%

 Raw Data, $X$ Sorted Data

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

%

## 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)

### 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

Sorted Data
(Ascending Order)
 The data values less than are:

The count of those values 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

th percentile

Sorted Data
(Ascending Order)

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.

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

standard deviations

Case 5
Given: Mean, Standard Deviation
To Calculate: the boundaries of usual and unusual data values