Calculate Root Mean Square from -6,4,3,-9,2,8

<-- Enter Number Set
<-- Probabilities (or counts for Weighted Average), check box if you are using these →

You entered a number set X of {-6,4,3,-9,2,8}

From the 6 numbers you entered, we want to calculate the root mean square:
Root Mean Square  =  A

where A = x12 + x22 + x32 + x42 + x52 + x62 and N = 6 number set items

A = -62 + 42 + 32 + -92 + 22 + 82
A = 36 + 16 + 9 + 81 + 4 + 64
A = 210

Calculate Root Mean Square (RMS):

RMS  =  210

RMS  =  14.491376746189

What is the Answer?

RMS = 5.9160797830996

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
Average Deviation (Mean Absolute Deviation)
Pearsons Skewness Coefficients
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?

  1. Root Mean Square = √A/√N
  2. Successive Ratio = n1/n0
  3. μ = ΣXi/n
  4. Mode = Highest Frequency Number
  5. Mid-Range = (Maximum Value in Number Set + Minimum Value in Number Set)/2
  6. Quartile: V = y(n + 1)/100
  7. σ2 = ΣE(Xi - 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
refers to disorder or uncertainty
expected value
predicted value of a variable or event
E(X) = ΣxI · P(x)
frequency distribution
frequency measurement of various outcomes
inner fence
ut-off values for upper and lower outliers in a dataset
A statistical measurement also known as the average
the value separating the higher half from the lower half of a data sample,
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.
an observation that lies an abnormal distance from other values in a random sample from a population
1 of 4 equal groups in the distribution of a number set
Difference between the largest and smallest values in a number set
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.
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

  1. 1,2,3,4,5
  2. (-6,4,3,-9,2,8)

Basic Statistics Calculator Video


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