You entered a number set X of {27.86,13.29,33.03,44.31,16.58,42.43,39.61,25.51,39.14,16.58,47.13,14.70,57.47,34.44}
From the 14 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
Ranked Data Calculation
Sort our number set in ascending order
and assign a ranking to each number:
Ranked Data Table
| Number Set Value | 13.29 | 14.70 | 16.58 | 16.58 | 25.51 | 27.86 | 33.03 | 34.44 | 39.14 | 39.61 | 42.43 | 44.31 | 47.13 | 57.47 |
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
Step 2: Using original number set, assign the rank value:
Since we have 14 numbers in our original number set, we assign ranks from lowest to highest (1 to 14)Our original number set in unsorted order was 27.86,13.29,33.03,44.31,16.58,42.43,39.61,25.51,39.14,16.58,47.13,14.70,57.47,34.44
Our respective ranked data set is 6,1,7,12,4,11,10,5,9,4,13,2,14,8
Root Mean Square Calculation
| Root Mean Square = | √A |
| √N |
where A = x12 + x22 + x32 + x42 + x52 + x62 + x72 + x82 + x92 + x102 + x112 + x122 + x132 + x142 and N = 14 number set items
Calculate A
A = 13.292 + 14.702 + 16.582 + 16.582 + 25.512 + 27.862 + 33.032 + 34.442 + 39.142 + 39.612 + 42.432 + 44.312 + 47.132 + 57.472
A = 176.6241 + 216.09 + 274.8964 + 274.8964 + 650.7601 + 776.1796 + 1090.9809 + 1186.1136 + 1531.9396 + 1568.9521 + 1800.3049 + 1963.3761 + 2221.2369 + 3302.8009
A = 17035.1516
Calculate Root Mean Square (RMS):
| RMS = | √17035.1516 |
| √14 |
| RMS = | 130.51877872552 |
| 3.7416573867739 |
RMS = 34.882610895074
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 = | ΣXi |
| n |
| μ = | 13.29 + 14.70 + 16.58 + 16.58 + 25.51 + 27.86 + 33.03 + 34.44 + 39.14 + 39.61 + 42.43 + 44.31 + 47.13 + 57.47 |
| 14 |
| μ = | 452.08 |
| 14 |
μ = 32.291428571429
Calculate the Median (Middle Value)
Since our number set contains 14 elements which is an even number, our median number is determined as follows:
Number Set = (n1,n2,n3,n4,n5,n6,n7,n8,n9,n10,n11,n12,n13,n14)
Median Number 1 = ½(n)
Median Number 1 = ½(14)
Median Number 1 = Number Set Entry 7
Median Number 2 = Median Number 1 + 1
Median Number 2 = Number Set Entry 7 + 1
Median Number 2 = Number Set Entry 8
For an even number set, we average the 2 median number entries:
Median = ½(n7 + n8)
Therefore, we sort our number set in ascending order and our median is the average of entry 7 and entry 8 of our number set highlighted in red:
(13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47)
Median = ½(33.03 + 34.44)
Median = ½(67.47)
Median = 33.735
Calculate the Mode - Highest Frequency Number
The highest frequency of occurence in our number set is 2 times by the following numbers in green:(27.86,13.29,33.03,44.31,16.58,42.43,39.61,25.51,39.14,16.58,47.13,14.70,57.47,34.44)
Our mode is denoted as: 16.58
Mode = 16.58
Calculate Harmonic Mean:
| Harmonic Mean = | N |
| 1/x1 + 1/x2 + 1/x3 + 1/x4 + 1/x5 + 1/x6 + 1/x7 + 1/x8 + 1/x9 + 1/x10 + 1/x11 + 1/x12 + 1/x13 + 1/x14 |
With N = 14 and each xi a member of the number set you entered, we have:
| Harmonic Mean = | 14 |
| 1/13.29 + 1/14.70 + 1/16.58 + 1/16.58 + 1/25.51 + 1/27.86 + 1/33.03 + 1/34.44 + 1/39.14 + 1/39.61 + 1/42.43 + 1/44.31 + 1/47.13 + 1/57.47 |
| Harmonic Mean = | 14 |
| 0.075244544770504 + 0.068027210884354 + 0.060313630880579 + 0.060313630880579 + 0.039200313602509 + 0.035893754486719 + 0.030275507114744 + 0.029036004645761 + 0.025549310168625 + 0.025246149962131 + 0.023568230025925 + 0.022568269013767 + 0.02121790791428 + 0.017400382808422 |
| Harmonic Mean = | 14 |
| 0.5338548471589 |
Harmonic Mean = 26.224356816288
Calculate Geometric Mean:
Geometric Mean = (x1 * x2 * x3 * x4 * x5 * x6 * x7 * x8 * x9 * x10 * x11 * x12 * x13 * x14)1/NGeometric Mean = (13.29 * 14.70 * 16.58 * 16.58 * 25.51 * 27.86 * 33.03 * 34.44 * 39.14 * 39.61 * 42.43 * 44.31 * 47.13 * 57.47)1/14
Geometric Mean = 3.4277862923141E+200.071428571428571
Geometric Mean = 29.294540856618
Calcualte Mid-Range:
| Mid-Range = | Maximum Value in Number Set + Minimum Value in Number Set |
| 2 |
| Mid-Range = | 57.47 + 13.29 |
| 2 |
| Mid-Range = | 70.76 |
| 2 |
Mid-Range = 35.38
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:
{57.47,47.13,44.31,42.43,39.61,39.14,34.44,33.03,27.86,25.51,16.58,16.58,14.70,13.29}| Stem | Leaf |
|---|---|
| 5 | 7.47 |
| 4 | 2.43,4.31,7.13 |
| 3 | 3.03,4.44,9.14,9.61 |
| 2 | 5.51,7.86 |
| 1 | 3.29,4.70,6.58,6.58 |
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 = | ΣXi |
| n |
| μ = | 13.29 + 14.70 + 16.58 + 16.58 + 25.51 + 27.86 + 33.03 + 34.44 + 39.14 + 39.61 + 42.43 + 44.31 + 47.13 + 57.47 |
| 14 |
| μ = | 452.08 |
| 14 |
μ = 32.291428571429
Calculate Variance denoted as σ2
Let's evaluate the square difference from the mean of each term (Xi - μ)2:
(X1 - μ)2 = (13.29 - 32.291428571429)2 = -19.0014285714292 = 361.0542877551
(X2 - μ)2 = (14.70 - 32.291428571429)2 = -17.5914285714292 = 309.45835918367
(X3 - μ)2 = (16.58 - 32.291428571429)2 = -15.7114285714292 = 246.8489877551
(X4 - μ)2 = (16.58 - 32.291428571429)2 = -15.7114285714292 = 246.8489877551
(X5 - μ)2 = (25.51 - 32.291428571429)2 = -6.78142857142862 = 45.987773469388
(X6 - μ)2 = (27.86 - 32.291428571429)2 = -4.43142857142862 = 19.637559183674
(X7 - μ)2 = (33.03 - 32.291428571429)2 = 0.738571428571432 = 0.54548775510204
(X8 - μ)2 = (34.44 - 32.291428571429)2 = 2.14857142857142 = 4.6163591836734
(X9 - μ)2 = (39.14 - 32.291428571429)2 = 6.84857142857142 = 46.902930612245
(X10 - μ)2 = (39.61 - 32.291428571429)2 = 7.31857142857142 = 53.561487755102
(X11 - μ)2 = (42.43 - 32.291428571429)2 = 10.1385714285712 = 102.79063061224
(X12 - μ)2 = (44.31 - 32.291428571429)2 = 12.0185714285712 = 144.44605918367
(X13 - μ)2 = (47.13 - 32.291428571429)2 = 14.8385714285712 = 220.18320204082
(X14 - μ)2 = (57.47 - 32.291428571429)2 = 25.1785714285712 = 633.96045918367
Adding our 14 sum of squared differences up, we have our variance numerator:
ΣE(Xi - μ)2 = 361.0542877551 + 309.45835918367 + 246.8489877551 + 246.8489877551 + 45.987773469388 + 19.637559183674 + 0.54548775510204 + 4.6163591836734 + 46.902930612245 + 53.561487755102 + 102.79063061224 + 144.44605918367 + 220.18320204082 + 633.96045918367
ΣE(Xi - μ)2 = 2436.8425714286
Now that we have the sum of squared differences from the means, calculate variance:
| Population | Sample | ||||||||
|---|---|---|---|---|---|---|---|---|---|
|
|
|
| ||||||
| Variance: σp2 = 174.06018367347 | Variance: σs2 = 187.44942857143 | ||||||||
| Standard Deviation: σp = √σp2 = √174.06018367347 | Standard Deviation: σs = √σs2 = √187.44942857143 | ||||||||
| Standard Deviation: σp = 13.1932 | Standard Deviation: σs = 13.6912 |
Calculate the Standard Error of the Mean:
| Population | Sample | ||||||||
|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
|
| ||||
| SEM = 3.526 | SEM = 3.6591 |
Calculate Skewness:
| Skewness = | E(Xi - μ)3 |
| (n - 1)σ3 |
Let's evaluate the square difference from the mean of each term (Xi - μ)3:
(X1 - μ)3 = (13.29 - 32.291428571429)3 = -19.0014285714293 = -6860.5472591866
(X2 - μ)3 = (14.70 - 32.291428571429)3 = -17.5914285714293 = -5443.8146214111
(X3 - μ)3 = (16.58 - 32.291428571429)3 = -15.7114285714293 = -3878.3502390437
(X4 - μ)3 = (16.58 - 32.291428571429)3 = -15.7114285714293 = -3878.3502390437
(X5 - μ)3 = (25.51 - 32.291428571429)3 = -6.78142857142863 = -311.86280094169
(X6 - μ)3 = (27.86 - 32.291428571429)3 = -4.43142857142863 = -87.02244083965
(X7 - μ)3 = (33.03 - 32.291428571429)3 = 0.738571428571433 = 0.40288167055393
(X8 - μ)3 = (34.44 - 32.291428571429)3 = 2.14857142857143 = 9.9185774460641
(X9 - μ)3 = (39.14 - 32.291428571429)3 = 6.84857142857143 = 321.21807050729
(X10 - μ)3 = (39.61 - 32.291428571429)3 = 7.31857142857143 = 391.99357395627
(X11 - μ)3 = (42.43 - 32.291428571429)3 = 10.1385714285713 = 1042.1501506501
(X12 - μ)3 = (44.31 - 32.291428571429)3 = 12.0185714285713 = 1736.0352798746
(X13 - μ)3 = (47.13 - 32.291428571429)3 = 14.8385714285713 = 3267.2041708542
(X14 - μ)3 = (57.47 - 32.291428571429)3 = 25.1785714285713 = 15962.218704446
Adding our 14 sum of cubed differences up, we have our skewness numerator:
ΣE(Xi - μ)3 = -6860.5472591866 + -5443.8146214111 + -3878.3502390437 + -3878.3502390437 + -311.86280094169 + -87.02244083965 + 0.40288167055393 + 9.9185774460641 + 321.21807050729 + 391.99357395627 + 1042.1501506501 + 1736.0352798746 + 3267.2041708542 + 15962.218704446
ΣE(Xi - μ)3 = 2271.1938089388
Now that we have the sum of cubed differences from the means, calculate skewness:
| Skewness = | E(Xi - μ)3 |
| (n - 1)σ3 |
| Skewness = | 2271.1938089388 |
| (14 - 1)13.19323 |
| Skewness = | 2271.1938089388 |
| (13)2296.4153347896 |
| Skewness = | 2271.1938089388 |
| 29853.399352264 |
Skewness = 0.076078230895554
Calculate Average Deviation (Mean Absolute Deviation) denoted below:
| AD = | Σ|Xi - μ| |
| n |
Let's evaluate the absolute value of the difference from the mean of each term |Xi - μ|:
|X1 - μ| = |13.29 - 32.291428571429| = |-19.001428571429| = 19.001428571429
|X2 - μ| = |14.70 - 32.291428571429| = |-17.591428571429| = 17.591428571429
|X3 - μ| = |16.58 - 32.291428571429| = |-15.711428571429| = 15.711428571429
|X4 - μ| = |16.58 - 32.291428571429| = |-15.711428571429| = 15.711428571429
|X5 - μ| = |25.51 - 32.291428571429| = |-6.7814285714286| = 6.7814285714286
|X6 - μ| = |27.86 - 32.291428571429| = |-4.4314285714286| = 4.4314285714286
|X7 - μ| = |33.03 - 32.291428571429| = |0.73857142857143| = 0.73857142857143
|X8 - μ| = |34.44 - 32.291428571429| = |2.1485714285714| = 2.1485714285714
|X9 - μ| = |39.14 - 32.291428571429| = |6.8485714285714| = 6.8485714285714
|X10 - μ| = |39.61 - 32.291428571429| = |7.3185714285714| = 7.3185714285714
|X11 - μ| = |42.43 - 32.291428571429| = |10.138571428571| = 10.138571428571
|X12 - μ| = |44.31 - 32.291428571429| = |12.018571428571| = 12.018571428571
|X13 - μ| = |47.13 - 32.291428571429| = |14.838571428571| = 14.838571428571
|X14 - μ| = |57.47 - 32.291428571429| = |25.178571428571| = 25.178571428571
Adding our 14 absolute value of differences from the mean, we have our average deviation numerator:
Σ|Xi - μ| = 19.001428571429 + 17.591428571429 + 15.711428571429 + 15.711428571429 + 6.7814285714286 + 4.4314285714286 + 0.73857142857143 + 2.1485714285714 + 6.8485714285714 + 7.3185714285714 + 10.138571428571 + 12.018571428571 + 14.838571428571 + 25.178571428571
Σ|Xi - μ| = 158.45714285714
Now that we have the absolute value of the differences from the means, calculate average deviation (mean absolute deviation):
| AD = | Σ|Xi - μ| |
| n |
| AD = | 158.45714285714 |
| 14 |
Average Deviation = 11.31837
Calculate the Median (Middle Value)
Since our number set contains 14 elements which is an even number, our median number is determined as follows:
Number Set = (n1,n2,n3,n4,n5,n6,n7,n8,n9,n10,n11,n12,n13,n14)
Median Number 1 = ½(n)
Median Number 1 = ½(14)
Median Number 1 = Number Set Entry 7
Median Number 2 = Median Number 1 + 1
Median Number 2 = Number Set Entry 7 + 1
Median Number 2 = Number Set Entry 8
For an even number set, we average the 2 median number entries:
Median = ½(n7 + n8)
Therefore, we sort our number set in ascending order and our median is the average of entry 7 and entry 8 of our number set highlighted in red:
(13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47)
Median = ½(33.03 + 34.44)
Median = ½(67.47)
Median = 33.735
Calculate the Mode - Highest Frequency Number
The highest frequency of occurence in our number set is 2 times by the following numbers in green:(27.86,13.29,33.03,44.31,16.58,42.43,39.61,25.51,39.14,16.58,47.13,14.70,57.47,34.44)
Our mode is denoted as: 16.58
Mode = 16.58
Calculate the Range
Range = Largest Number in the Number Set - Smallest Number in the Number SetRange = 57.47 - 13.29
Range = 44.18
Calculate Pearsons Skewness Coefficient 1:
| PSC1 = | μ - Mode |
| σ |
| PSC1 = | 3(32.291428571429 - 16.58) |
| 13.1932 |
| PSC1 = | 3 x 15.711428571429 |
| 13.1932 |
| PSC1 = | 47.134285714286 |
| 13.1932 |
PSC1 = 3.5726
Calculate Pearsons Skewness Coefficient 2:
| PSC2 = | μ - Median |
| σ |
| PSC1 = | 3(32.291428571429 - 33.735) |
| 13.1932 |
| PSC2 = | 3 x -1.4435714285714 |
| 13.1932 |
| PSC2 = | -4.3307142857143 |
| 13.1932 |
PSC2 = -0.3283
Calculate Entropy:
Entropy = Ln(n)Entropy = Ln(14)
Entropy = 2.6390573296153
Calculate Mid-Range:
| Mid-Range = | Smallest Number in the Set + Largest Number in the Set |
| 2 |
| Mid-Range = | 57.47 + 13.29 |
| 2 |
| Mid-Range = | 70.76 |
| 2 |
Mid-Range = 35.38
Calculate the Quartile Items
We need to sort our number set from lowest to highest shown below:{13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47}
Calculate Upper Quartile (UQ) when y = 75%:
| V = | y(n + 1) |
| 100 |
| V = | 75(14 + 1) |
| 100 |
| V = | 75(15) |
| 100 |
| V = | 1125 |
| 100 |
V = 11 ← Rounded down to the nearest integer
Upper quartile (UQ) point = Point # 11 in the dataset which is 42.43
13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
Calculate Lower Quartile (LQ) when y = 25%:
| V = | y(n + 1) |
| 100 |
| V = | 25(14 + 1) |
| 100 |
| V = | 25(15) |
| 100 |
| V = | 375 |
| 100 |
V = 4 ← Rounded up to the nearest integer
Lower quartile (LQ) point = Point # 4 in the dataset which is 16.58
13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
Calculate Inter-Quartile Range (IQR):
IQR = UQ - LQIQR = 42.43 - 16.58
IQR = 25.85
Calculate Lower Inner Fence (LIF):
Lower Inner Fence (LIF) = LQ - 1.5 x IQRLower Inner Fence (LIF) = 16.58 - 1.5 x 25.85
Lower Inner Fence (LIF) = 16.58 - 38.775
Lower Inner Fence (LIF) = -22.195
Calculate Upper Inner Fence (UIF):
Upper Inner Fence (UIF) = UQ + 1.5 x IQRUpper Inner Fence (UIF) = 42.43 + 1.5 x 25.85
Upper Inner Fence (UIF) = 42.43 + 38.775
Upper Inner Fence (UIF) = 81.205
Calculate Lower Outer Fence (LOF):
Lower Outer Fence (LOF) = LQ - 3 x IQRLower Outer Fence (LOF) = 16.58 - 3 x 25.85
Lower Outer Fence (LOF) = 16.58 - 77.55
Lower Outer Fence (LOF) = -60.97
Calculate Upper Outer Fence (UOF):
Upper Outer Fence (UOF) = UQ + 3 x IQRUpper Outer Fence (UOF) = 42.43 + 3 x 25.85
Upper Outer Fence (UOF) = 42.43 + 77.55
Upper Outer Fence (UOF) = 119.98
Calculate Suspect Outliers:
Suspect Outliers are values between the inner and outer fencesWe wish to mark all values in our dataset (v) in red below such that -60.97 < v < -22.195 and 81.205 < v < 119.98
13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
Calculate Highly Suspect Outliers:
Highly Suspect Outliers are values outside the outer fencesWe wish to mark all values in our dataset (v) in red below such that v < -60.97 or v > 119.98
13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
Calculate weighted average
27.86,13.29,33.03,44.31,16.58,42.43,39.61,25.51,39.14,16.58,47.13,14.70,57.47,34.44
Weighted-Average Formula:
Multiply each value by each probability amount
We do this by multiplying each Xi x pi to get a weighted score Y
| Weighted Average = | X1p1 + X2p2 + X3p3 + X4p4 + X5p5 + X6p6 + X7p7 + X8p8 + X9p9 + X10p10 + X11p11 + X12p12 + X13p13 + X14p14 |
| n |
| Weighted Average = | 27.86 x 0.2 + 13.29 x 0.4 + 33.03 x 0.6 + 44.31 x 0.8 + 16.58 x 0.9 + 42.43 x + 39.61 x + 25.51 x + 39.14 x + 16.58 x + 47.13 x + 14.70 x + 57.47 x + 34.44 x |
| 14 |
| Weighted Average = | 5.572 + 5.316 + 19.818 + 35.448 + 14.922 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 |
| 14 |
| Weighted Average = | 81.076 |
| 14 |
Weighted Average = 5.7911428571429
Frequency Distribution Table
Show the freqency distribution table for this number set
13.29, 14.70, 16.58, 16.58, 25.51, 27.86, 33.03, 34.44, 39.14, 39.61, 42.43, 44.31, 47.13, 57.47
Determine the Number of Intervals using Sturges Rule:
We need to choose the smallest integer k such that 2k ≥ n where n = 14
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 14
Therefore, we use 4 intervals
Our maximum value in our number set of 57.47 - 13.29 = 44.18
Each interval size is the difference of the maximum and minimum value divided by the number of intervals
| Interval Size = | 44.18 |
| 4 |
Add 1 to this giving us 11 + 1 = 12
Frequency Distribution Table
| Class Limits | Class Boundaries | FD | CFD | RFD | CRFD |
|---|---|---|---|---|---|
| 13.29 - 25.29 | 12.79 - 25.79 | 4 | 4 | 4/14 = 28.57% | 4/14 = 28.57% |
| 25.29 - 37.29 | 24.79 - 37.79 | 4 | 4 + 4 = 8 | 4/14 = 28.57% | 8/14 = 57.14% |
| 37.29 - 49.29 | 36.79 - 49.79 | 5 | 4 + 4 + 5 = 13 | 5/14 = 35.71% | 13/14 = 92.86% |
| 49.29 - 61.29 | 48.79 - 61.79 | 1 | 4 + 4 + 5 + 1 = 14 | 1/14 = 7.14% | 14/14 = 100% |
| 14 | 100% |
Successive Ratio Calculation
Go through our 14 numbers
Determine the ratio of each number to the next one
Successive Ratio 1: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
13.29:14.70 → 0.9041
Successive Ratio 2: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
14.70:16.58 → 0.8866
Successive Ratio 3: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
16.58:16.58 → 1
Successive Ratio 4: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
16.58:25.51 → 0.6499
Successive Ratio 5: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
25.51:27.86 → 0.9156
Successive Ratio 6: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
27.86:33.03 → 0.8435
Successive Ratio 7: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
33.03:34.44 → 0.9591
Successive Ratio 8: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
34.44:39.14 → 0.8799
Successive Ratio 9: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
39.14:39.61 → 0.9881
Successive Ratio 10: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
39.61:42.43 → 0.9335
Successive Ratio 11: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
42.43:44.31 → 0.9576
Successive Ratio 12: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
44.31:47.13 → 0.9402
Successive Ratio 13: 13.29,14.70,16.58,16.58,25.51,27.86,33.03,34.44,39.14,39.61,42.43,44.31,47.13,57.47
47.13:57.47 → 0.8201
Successive Ratio Answer
Successive Ratio = 13.29:14.70,14.70:16.58,16.58:16.58,16.58:25.51,25.51:27.86,27.86:33.03,33.03:34.44,34.44:39.14,39.14:39.61,39.61:42.43,42.43:44.31,44.31:47.13,47.13:57.47 or 0.9041,0.8866,1,0.6499,0.9156,0.8435,0.9591,0.8799,0.9881,0.9335,0.9576,0.9402,0.8201
Final Answers
6,1,7,12,4,11,10,5,9,4,13,2,14,8
RMS = 34.882610895074
Harmonic Mean = 26.224356816288Geometric Mean = 29.294540856618
Mid-Range = 35.38
Weighted Average = 5.7911428571429
Successive Ratio = Successive Ratio = 13.29:14.70,14.70:16.58,16.58:16.58,16.58:25.51,25.51:27.86,27.86:33.03,33.03:34.44,34.44:39.14,39.14:39.61,39.61:42.43,42.43:44.31,44.31:47.13,47.13:57.47 or 0.9041,0.8866,1,0.6499,0.9156,0.8435,0.9591,0.8799,0.9881,0.9335,0.9576,0.9402,0.8201
RMS = 34.882610895074
Harmonic Mean = 26.224356816288Geometric Mean = 29.294540856618
Mid-Range = 35.38
Weighted Average = 5.7911428571429
Successive Ratio = Successive Ratio = 13.29:14.70,14.70:16.58,16.58:16.58,16.58:25.51,25.51:27.86,27.86:33.03,33.03:34.44,34.44:39.14,39.14:39.61,39.61:42.43,42.43:44.31,44.31:47.13,47.13:57.47 or 0.9041,0.8866,1,0.6499,0.9156,0.8435,0.9591,0.8799,0.9881,0.9335,0.9576,0.9402,0.8201
You have 2 free calculationss remaining
What is the Answer?
6,1,7,12,4,11,10,5,9,4,13,2,14,8
RMS = 34.882610895074
Harmonic Mean = 26.224356816288Geometric Mean = 29.294540856618
Mid-Range = 35.38
Weighted Average = 5.7911428571429
Successive Ratio = Successive Ratio = 13.29:14.70,14.70:16.58,16.58:16.58,16.58:25.51,25.51:27.86,27.86:33.03,33.03:34.44,34.44:39.14,39.14:39.61,39.61:42.43,42.43:44.31,44.31:47.13,47.13:57.47 or 0.9041,0.8866,1,0.6499,0.9156,0.8435,0.9591,0.8799,0.9881,0.9335,0.9576,0.9402,0.8201
RMS = 34.882610895074
Harmonic Mean = 26.224356816288Geometric Mean = 29.294540856618
Mid-Range = 35.38
Weighted Average = 5.7911428571429
Successive Ratio = Successive Ratio = 13.29:14.70,14.70:16.58,16.58:16.58,16.58:25.51,25.51:27.86,27.86:33.03,33.03:34.44,34.44:39.14,39.14:39.61,39.61:42.43,42.43:44.31,44.31:47.13,47.13:57.47 or 0.9041,0.8866,1,0.6499,0.9156,0.8435,0.9591,0.8799,0.9881,0.9335,0.9576,0.9402,0.8201
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.
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 = ΣXi/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(Xi - μ)2/n
For more math formulas, check out our Formula Dossier
Successive Ratio = n1/n0
μ = ΣXi/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(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
- entropy
- 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
- 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
Basic Statistics Calculator Video
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