Adding our 15 absolute value of differences from the mean, we have our average deviation numerator: Σ|X_{i} - μ| = 0.92 + 0.62 + 1.38 + 1.02 + 1.28 + 0.28 + 0.92 + 0.92 + 1.08 + 0.42 + 1.08 + 0.78 + 0.52 + 0.28 + 0.82 Σ|X_{i} - μ| = 12.32
Now that we have the absolute value of the differences from the means, calculate average deviation (mean absolute deviation):
AD =
Σ|X_{i} - μ|
n
AD =
12.32
15
Average Deviation = 0.82133
Calculate the Median (Middle Value) Since our number set contains 15 elements which is an odd number, our median number is determined as follows: Number Set = (n_{1},n_{2},n_{3},n_{4},n_{5},n_{6},n_{7},n_{8},n_{9},n_{10},n_{11},n_{12},n_{13},n_{14},n_{15}) Median Number = Entry ½(n + 1) Median Number = Entry ½(16) Median Number = n_{8}
Therefore, we sort our number set in ascending order and our median is entry 8 of our number set highlighted in red: (2.9,3.0,3.2,3.2,3.5,4.0,4.0,4.7,4.8,4.9,5.1,5.2,5.2,5.2,5.3) Median = 4.7
The highest frequency of occurence in our number set is 3 times by the following numbers in green: (5.2,4.9,2.9,5.3,3.0,4.0,5.2,5.2,3.2,4.7,3.2,3.5,4.8,4.0,5.1) Our mode is denoted as: 5.2 Mode = 5.2
Smallest Number in the Set + Largest Number in the Set
2
Mid-Range =
5.3 + 2.9
2
Mid-Range =
8.2
2
Mid-Range = 4.1
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 = σ^{2} 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 = n_{1}/n_{0} 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 σ^{2} = ΣE(X_{i} - μ)^{2}/n
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