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Calculate Calculate from 36,1,74,82,45,34,41,38,6,21,90,33

David Miller • Oct 10, 2026 • 12 min read

Calculate Calculate from 36,1,74,82,45,34,41,38,6,21,90,33

Explore in-depth coverage about Calculate Calculate from 36,1,74,82,45,34,41,38,6,21,90,33.

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 < -51 or v > 117
1,6,21,33,34,36,38,41,45,74,82,90

Calculate weighted average

36,1,74,82,45,34,41,38,6,21,90,33

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 =	X₁p₁ + X₂p₂ + X₃p₃ + X₄p₄ + X₅p₅ + X₆p₆ + X₇p₇ + X₈p₈ + X₉p₉ + X₁₀p₁₀ + X₁₁p₁₁ + X₁₂p₁₂
	n

Weighted Average =	36 x + 1 x + 74 x + 82 x + 45 x + 34 x + 41 x + 38 x + 6 x + 21 x + 90 x + 33 x
	12

Weighted Average =	0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0
	12

Weighted Average =	0
	12

Weighted Average = 0

Frequency Distribution Table

Show the freqency distribution table for this number set

1, 6, 21, 33, 34, 36, 38, 41, 45, 74, 82, 90

Determine the Number of Intervals using Sturges Rule:

We need to choose the smallest integer k such that 2^k ≥ n where n = 12

For k = 1, we have 2¹ = 2

For k = 2, we have 2² = 4

For k = 3, we have 2³ = 8

For k = 4, we have 2⁴ = 16 ← Use this since it is greater than our n value of 12

Therefore, we use 4 intervals

Our maximum value in our number set of 90 - 1 = 89

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

Interval Size =	89
	4

Add 1 to this giving us 22 + 1 = 23

Frequency Distribution Table

Class Limits	Class Boundaries	FD	CFD	RFD	CRFD
1 - 24	0.5 - 24.5	3	3	3/12 = 25%	3/12 = 25%
24 - 47	23.5 - 47.5	6	3 + 6 = 9	6/12 = 50%	9/12 = 75%
47 - 70	46.5 - 70.5		3 + 6 + = 9	/12 = 0%	9/12 = 75%
70 - 93	69.5 - 93.5	3	3 + 6 + + 3 = 12	3/12 = 25%	12/12 = 100%
		12		100%

Successive Ratio Calculation

Go through our 12 numbers

Determine the ratio of each number to the next one

Successive Ratio 1: 1,6,21,33,34,36,38,41,45,74,82,90

1:6 → 0.1667

Successive Ratio 2: 1,6,21,33,34,36,38,41,45,74,82,90

6:21 → 0.2857

Successive Ratio 3: 1,6,21,33,34,36,38,41,45,74,82,90

21:33 → 0.6364

Successive Ratio 4: 1,6,21,33,34,36,38,41,45,74,82,90

33:34 → 0.9706

Successive Ratio 5: 1,6,21,33,34,36,38,41,45,74,82,90

34:36 → 0.9444

Successive Ratio 6: 1,6,21,33,34,36,38,41,45,74,82,90

36:38 → 0.9474

Successive Ratio 7: 1,6,21,33,34,36,38,41,45,74,82,90

38:41 → 0.9268

Successive Ratio 8: 1,6,21,33,34,36,38,41,45,74,82,90

41:45 → 0.9111

Successive Ratio 9: 1,6,21,33,34,36,38,41,45,74,82,90

45:74 → 0.6081

Successive Ratio 10: 1,6,21,33,34,36,38,41,45,74,82,90

74:82 → 0.9024

Successive Ratio 11: 1,6,21,33,34,36,38,41,45,74,82,90

82:90 → 0.9111

Successive Ratio Answer

Successive Ratio = 1:6,6:21,21:33,33:34,34:36,36:38,38:41,41:45,45:74,74:82,82:90 or 0.1667,0.2857,0.6364,0.9706,0.9444,0.9474,0.9268,0.9111,0.6081,0.9024,0.9111

Final Answers

6,1,10,11,9,5,8,7,2,3,12,4
RMS = 49.555524414539
Harmonic Mean = 8.5014357092882Geometric Mean = 27.59377778885
Mid-Range = 45.5
Weighted Average = 0
Successive Ratio = Successive Ratio = 1:6,6:21,21:33,33:34,34:36,36:38,38:41,41:45,45:74,74:82,82:90 or 0.1667,0.2857,0.6364,0.9706,0.9444,0.9474,0.9268,0.9111,0.6081,0.9024,0.9111

You have 1 free calculations remaining

What is the Answer?

6,1,10,11,9,5,8,7,2,3,12,4
RMS = 49.555524414539
Harmonic Mean = 8.5014357092882Geometric Mean = 27.59377778885
Mid-Range = 45.5
Weighted Average = 0
Successive Ratio = Successive Ratio = 1:6,6:21,21:33,33:34,34:36,36:38,38:41,41:45,45:74,74:82,82:90 or 0.1667,0.2857,0.6364,0.9706,0.9444,0.9474,0.9268,0.9111,0.6081,0.9024,0.9111

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

Author

David Miller

David Miller brings 15 years of experience in global economics, personal finance strategy, and market dynamics. He specializes in turning complex economic trends into actionable insights for everyday readers.