Calculate Calculate from 36

You entered a number set X of {36}

From the 1 numbers you entered, we want to calculate the mean, variance, standard deviation, standard error of the mean, skewness, average deviation (mean absolute deviation), median, mode, range, Pearsons Skewness Coefficient of that number set, entropy, mid-range

Sort Ascending from Lowest to Highest

Rank Ascending

36 is the 1st lowest/smallest number

Sort Descending from Highest to Lowest

Rank Descending

36 is the 1st highest/largest number

Ranked Data Calculation

Sort our number set in ascending order

and assign a ranking to each number:

Ranked Data Table

Number Set Value	36
Rank	1

Step 2: Using original number set, assign the rank value:

Since we have 1 numbers in our original number set,
we assign ranks from lowest to highest (1 to 1)

Our original number set in unsorted order was 36

Our respective ranked data set is 1

Root Mean Square Calculation

Root Mean Square =	√A
	√N

where A = x₁² and N = 1 number set items

Calculate A

A = 36²

A = 1296

Calculate Root Mean Square (RMS):

RMS =	√1296
	√1

RMS =	36
	1

RMS = 36

Central Tendency Calculation

Central tendency contains:
Mean, median, mode, harmonic mean,
geometric mean, mid-range, weighted-average:

Calculate Mean (Average) denoted as μ

μ =	Sum of your number Set
	Total Numbers Entered

μ =	ΣX_i
	n

μ =	36
	1

μ =	36
	1

μ = 36

Calculate the Median (Middle Value)

Since our number set contains 1 elements which is an odd number,
our median number is determined as follows:

Number Set = (n₁)

Median Number = Entry ½(n + 1)

Median Number = Entry ½(2)

Median Number = n₁

Therefore, we sort our number set in ascending order

Our median is entry 1 of our number set highlighted in red:

(36)

Median = 36

Calculate the Mode - Highest Frequency Number

The highest frequency of occurence in our number set is 1 times
by the following numbers in green:

()

Since the maximum frequency of any number is 1, no mode exists.

Mode = N/A

Calculate Harmonic Mean:

Harmonic Mean =	N
	1/x₁

With N = 1 and each x_i a member of the number set you entered, we have:

Harmonic Mean =	1
	1/36

Harmonic Mean =	1
	0.027777777777778

Harmonic Mean =	1
	0.027777777777778

Harmonic Mean = 36

Calculate Geometric Mean:

Geometric Mean = (x₁)^1/N

Geometric Mean = (36)^1/1

Geometric Mean = 36¹

Geometric Mean = 36

Calculate Mid-Range:

Mid-Range =	Maximum Value in Number Set + Minimum Value in Number Set
	2

Mid-Range =	36 + 36
	2

Mid-Range =	72
	2

Mid-Range = 36

Stem and Leaf Plot

Take the first digit of each value in our number set

Use this as our stem value

Use the remaining digits for our leaf portion

Sort our number set in descending order:

{36}

Stem	Leaf
3	6

Basic Stats Calculations

Mean, Variance, Standard Deviation, Median, Mode

Calculate Mean (Average) denoted as μ

μ =	Sum of your number Set
	Total Numbers Entered

μ =	ΣX_i
	n

μ =	36
	1

μ =	36
	1

μ = 36

Calculate Variance denoted as σ²

Let's evaluate the square difference from the mean of each term (X_i - μ)²:

(X₁ - μ)² = (36 - 36)² = 0² = 0

Adding our 1 sum of squared differences up

ΣE(X_i - μ)² = 0

Use the sum of squared differences to calculate variance

Population

Sample

σ² =	ΣE(X_i - μ)²
	n

σ² =	ΣE(X_i - μ)²
	n - 1

σ² =	0
	1

σ² =	0
	0

Variance: σ_p² = 0

Variance: σ_s² = NAN

Standard Deviation: σ_p = √σ_p² = √0

Standard Deviation: σ_s = √σ_s² = √NAN

Standard Deviation: σ_p = 0

Standard Deviation: σ_s = NAN

Calculate the Standard Error of the Mean:

Population

Sample

SEM =	σ_p
	√n

SEM =	σ_s
	√n

SEM =	0
	√1

SEM =	NAN
	√1

SEM =	0
	1

SEM =	NAN
	1

SEM = 0

SEM = NAN

Calculate Skewness:

Skewness =	E(X_i - μ)³
	(n - 1)σ³

Let's evaluate the square difference from the mean of each term (X_i - μ)³:

(X₁ - μ)³ = (36 - 36)³ = 0³ = 0

Add our 1 sum of cubed differences up

ΣE(X_i - μ)³ = 0

Calculate skewnes

Skewness =	E(X_i - μ)³
	(n - 1)σ³

Skewness =	0
	(1 - 1)0³

Skewness =	0
	(0)0

Skewness =	0
	0

Skewness = NAN

Calculate Average Deviation (Mean Absolute Deviation) denoted below:

AD =	Σ\|X_i - μ\|
	n

Evaluate the absolute value of the difference from the mean

|X_i - μ|:

|X₁ - μ| = |36 - 36| = |0| = 0

Average deviation numerator:

Σ|X_i - μ| = 0

Calculate average deviation (mean absolute deviation)

AD =	Σ\|X_i - μ\|
	n

AD =	0
	1

Average Deviation = 0

Calculate the Median (Middle Value)

Since our number set contains 1 elements which is an odd number,
our median number is determined as follows:

Number Set = (n₁)

Median Number = Entry ½(n + 1)

Median Number = Entry ½(2)

Median Number = n₁

Therefore, we sort our number set in ascending order

Our median is entry 1 of our number set highlighted in red:

(36)

Median = 36

Calculate the Mode - Highest Frequency Number

The highest frequency of occurence in our number set is 1 times
by the following numbers in green:

()

Since the maximum frequency of any number is 1, no mode exists.

Mode = N/A

Calculate the Range

Range = Largest Number in the Number Set - Smallest Number in the Number Set

Range = 36 - 36

Range = 0

Calculate Pearsons Skewness Coefficient 1:

PSC1 =	μ - Mode
	σ

PSC1 =	3(36 - N/A)
	0

Since no mode exists, we do not have a Pearsons Skewness Coefficient 1

Calculate Pearsons Skewness Coefficient 2:

PSC2 =	μ - Median
	σ

PSC1 =	3(36 - 36)
	0

PSC2 =	3 x 0
	0

PSC2 =	0
	0

PSC2 = NAN

Calculate Entropy:

Entropy = Ln(n)

Entropy = Ln(1)

Entropy = 0

Calculate Mid-Range:

Mid-Range =	Smallest Number in the Set + Largest Number in the Set
	2

Mid-Range =	36 + 36
	2

Mid-Range =	72
	2

Mid-Range = 36

Calculate the Quartile Items

We need to sort our number set from lowest to highest shown below:

{36}

Calculate Upper Quartile (UQ) when y = 75%:

V =	y(n + 1)
	100

V =	75(1 + 1)
	100

V =	75(2)
	100

V =	150
	100

V = 1 ← Rounded down to the nearest integer

Upper quartile (UQ) point = Point # 1 in the dataset which is 36

Calculate Lower Quartile (LQ) when y = 25%:

V =	y(n + 1)
	100

V =	25(1 + 1)
	100

V =	25(2)
	100

V =	50
	100

V = 1 ← Rounded up to the nearest integer

Lower quartile (LQ) point = Point # 1 in the dataset which is 36

Calculate Inter-Quartile Range (IQR):

IQR = UQ - LQ

IQR = 36 - 36

IQR = 0

Calculate Lower Inner Fence (LIF):

Lower Inner Fence (LIF) = LQ - 1.5 x IQR

Lower Inner Fence (LIF) = 36 - 1.5 x 0

Lower Inner Fence (LIF) = 36 - 0

Lower Inner Fence (LIF) = 36

Calculate Upper Inner Fence (UIF):

Upper Inner Fence (UIF) = UQ + 1.5 x IQR

Upper Inner Fence (UIF) = 36 + 1.5 x 0

Upper Inner Fence (UIF) = 36 + 0

Upper Inner Fence (UIF) = 36

Calculate Lower Outer Fence (LOF):

Lower Outer Fence (LOF) = LQ - 3 x IQR

Lower Outer Fence (LOF) = 36 - 3 x 0

Lower Outer Fence (LOF) = 36 - 0

Lower Outer Fence (LOF) = 36

Calculate Upper Outer Fence (UOF):

Upper Outer Fence (UOF) = UQ + 3 x IQR

Upper Outer Fence (UOF) = 36 + 3 x 0

Upper Outer Fence (UOF) = 36 + 0

Upper Outer Fence (UOF) = 36

Calculate Suspect Outliers:

Suspect Outliers are values between the inner and outer fences

We wish to mark all values in our dataset (v) in red below such that 36 < v < 36 and 36 < v < 36

Calculate Highly Suspect Outliers:

Highly Suspect Outliers are values outside the outer fences

We wish to mark all values in our dataset (v) in red below such that v < 36 or v > 36

Calculate weighted average

Array

Weighted-Average Formula:

Multiply each value by each probability amount

We do this by multiplying each X_i x p_i to get a weighted score Y

Weighted Average =
	n

Weighted Average =
	0

Weighted Average =
	0

Weighted Average =	0
	0

Weighted Average = NAN

Frequency Distribution Table

Show the freqency distribution table for this number set

Determine the Number of Intervals using Sturges Rule:

We need to choose the smallest integer k such that 2^k ≥ n where n = 0

Therefore, we use 0 intervals

Our maximum value in our number set of 36 - 36 = 0

Each interval size is the difference of the maximum and minimum value divided by the number of intervals

Interval Size =	0
	0

Add 1 to this giving us NAN + 1 = NAN

Frequency Distribution Table

Class Limits	Class Boundaries	FD	CFD	RFD	CRFD
		0		100%

Successive Ratio Calculation

Go through our 1 numbers

Determine the ratio of each number to the next one

Successive Ratio Answer

Successive Ratio = or

Final Answers

1
RMS = 36
Harmonic Mean = 36Geometric Mean = 36
Mid-Range = 36
Weighted Average = NAN
Successive Ratio = Successive Ratio = or

Common Core State Standards In This Lesson

6.SP.A.2, 6.SP.A.3, 6.SP.B.5, 6.SP.B.5.A, 6.SP.B.5.B, 6.SP.B.5.C, 6.SP.B.5.D, 7.SP.A.1, 7.SP.A.2, 7.SP.B.3, 7.SP.B.4, HSS.ID.A.2, HSS.ID.A.4, HSS.MD.A.2

What is the Answer?

1
RMS = 36
Harmonic Mean = 36Geometric Mean = 36
Mid-Range = 36
Weighted Average = NAN
Successive Ratio = Successive Ratio = or

How does the Basic Statistics Calculator work?

Free Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ²
Standard Deviation = σ
Standard Error of the Mean
Skewness
Mid-Range
Average Deviation (Mean Absolute Deviation)
Median
Mode
Range
Pearsons Skewness Coefficients
Entropy
Upper Quartile (hinge) (75th Percentile)
Lower Quartile (hinge) (25th Percentile)
InnerQuartile Range
Inner Fences (Lower Inner Fence and Upper Inner Fence)
Outer Fences (Lower Outer Fence and Upper Outer Fence)
Suspect Outliers
Highly Suspect Outliers
Stem and Leaf Plot
Ranked Data Set
Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range
Root Mean Square
Weighted Average (Weighted Mean)
Frequency Distribution
Successive Ratio
This calculator has 2 inputs.

What 8 formulas are used for the Basic Statistics Calculator?

Root Mean Square = √A/√N
Successive Ratio = n₁/n₀
μ = ΣX_i/n
Mode = Highest Frequency Number
Mid-Range = (Maximum Value in Number Set + Minimum Value in Number Set)/2
Quartile: V = y(n + 1)/100
σ² = ΣE(X_i - μ)²/n

For more math formulas, check out our Formula Dossier

What 20 concepts are covered in the Basic Statistics Calculator?

average deviation: Mean of the absolute values of the distance from the mean for each number in a number set
basic statistics
central tendency: a central or typical value for a probability distribution. Typical measures are the mode, median, mean
entropy: refers to disorder or uncertainty
expected value: predicted value of a variable or event
E(X) = Σx_I · P(x)
frequency distribution: frequency measurement of various outcomes
inner fence: ut-off values for upper and lower outliers in a dataset
mean: A statistical measurement also known as the average
median: the value separating the higher half from the lower half of a data sample,
mode: the number that occurs the most in a number set
outer fence: start with the IQR and multiply this number by 3. We then subtract this number from the first quartile and add it to the third quartile. These two numbers are our outer fences.
outlier: an observation that lies an abnormal distance from other values in a random sample from a population
quartile: 1 of 4 equal groups in the distribution of a number set
range: Difference between the largest and smallest values in a number set
rank: the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
sample space: the set of all possible outcomes or results of that experiment.
standard deviation: a measure of the amount of variation or dispersion of a set of values. The square root of variance
stem and leaf plot: a technique used to classify either discrete or continuous variables. A stem and leaf plot is used to organize data as they are collected. A stem and leaf plot looks something like a bar graph. Each number in the data is broken down into a stem and a leaf, thus the name.
variance: How far a set of random numbers are spead out from the mean
weighted average: An average of numbers using probabilities for each event as a weighting

Example calculations for the Basic Statistics Calculator

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Calculate Calculate from 36

Sort Ascending from Lowest to Highest

Sort Descending from Highest to Lowest

Ranked Data Calculation

Ranked Data Table

Step 2: Using original number set, assign the rank value:

Root Mean Square Calculation

Calculate A

Calculate Root Mean Square (RMS):

Central Tendency Calculation

Calculate Mean (Average) denoted as μ

Calculate the Median (Middle Value)

Therefore, we sort our number set in ascending order

Calculate the Mode - Highest Frequency Number

Calculate Harmonic Mean:

Calculate Geometric Mean:

Calculate Mid-Range:

Stem and Leaf Plot

Sort our number set in descending order:

Basic Stats Calculations

Calculate Mean (Average) denoted as μ

Calculate Variance denoted as σ2

Adding our 1 sum of squared differences up

Use the sum of squared differences to calculate variance

Calculate the Standard Error of the Mean:

Calculate Skewness:

Add our 1 sum of cubed differences up

Calculate skewnes

Calculate Average Deviation (Mean Absolute Deviation) denoted below:

Average deviation numerator:

Calculate the Median (Middle Value)

Therefore, we sort our number set in ascending order

Calculate the Mode - Highest Frequency Number

Calculate the Range

Calculate Pearsons Skewness Coefficient 1:

Calculate Pearsons Skewness Coefficient 2:

Calculate Entropy:

Calculate Mid-Range:

Calculate the Quartile Items

Calculate Upper Quartile (UQ) when y = 75%:

Calculate Lower Quartile (LQ) when y = 25%:

Calculate Inter-Quartile Range (IQR):

Calculate Lower Inner Fence (LIF):

Calculate Upper Inner Fence (UIF):

Calculate Lower Outer Fence (LOF):

Calculate Upper Outer Fence (UOF):

Calculate Suspect Outliers:

Calculate Highly Suspect Outliers:

Calculate weighted average

Weighted-Average Formula:

Frequency Distribution Table

Determine the Number of Intervals using Sturges Rule:

Frequency Distribution Table

Successive Ratio Calculation

Successive Ratio Answer

Final Answers

Common Core State Standards In This Lesson

What is the Answer?

How does the Basic Statistics Calculator work?

What 8 formulas are used for the Basic Statistics Calculator?

What 20 concepts are covered in the Basic Statistics Calculator?

Example calculations for the Basic Statistics Calculator

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Calculate Variance denoted as σ²