Statistics Calculator
Compute Mean, Median, Mode and Min, Max, Quartiles (Q1, Q2, Q3) along with Variance, Standard Deviation, Standard Error. Plot 3 sigma with histogram.
Stat Results
| Metric | Result |
|---|---|
| Count | 12 |
| Sum | 2218.15 |
| Min | 50.78 |
| Max | 469.82 |
| Range | 419.04 |
| Mean | 184.846 |
| Median | 151.05 |
| Mode | 378.32, 257.63, 469.82, 184.9, 50.78, 240.71, 57.35, 87.8, 117.2, 105.11, 53.82, 214.71 |
| Quartile | 64.963 151.05 253.4 |
| Outlier | none |
| Variance | 16641.75 |
| Standard Deviation | 129.003 |
| Standard Error | 37.24 |
| Sample Variance | 18154.636 |
| Sample Standard Deviation | 134.739 |
| Sample Standard Error | 38.896 |
Population Statistics vs Sampling Statistics
In Population Statistics, the dataset represents the full data and the exact variance, standard deviation is calculated
Example is Scores of Students in a class, temperature recorded in a month
Population Statistics
| Metric | Formula | Description |
|---|---|---|
| Variance | S2 = 1 n - 1 ∑ i = 1 n ( x i - x ¯ ) 2 | where, n is Number of observations in sample, xi is ith observation in the sample and x ¯ is Sample mean |
| Standard Deviation | S = 1 n - 1 ∑ i = Square root(1 n ( x i - x ¯ ) 2) | where, n is Number of observations in sample, xi is ith observation in the sample and x ¯ is Sample mean |
| Standard Error | SE = SD/Square root(n) | where, SE is Standard Error, SD is standard deviation and n is total numbers |
In Sample Statistics, it represents a sampling of the data and that is used to project for an entire category
Example is Average Height of Male and Females in different countries
Sample Statistics
| Metric | Formula | Description |
|---|---|---|
| Sample Variance | S2 = (1/ n - 1 ) * ∑ i( x i - x ¯ ) | where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean |
| Sample Standard Deviation | S = Square root((1/ n - 1 ) * ∑ i( x i - x ¯ ) 2) | where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean |
| Sample Standard Error | SSE = SSD/Square root(n) | where, SSE is Sample Standard Error, SSD is sample standard deviation and n is total numbers |
Histogram Chart
| Class | Range | Frequency |
|---|---|---|
| 1 | 0 - 43 | 0 |
| 2 | 44 - 87 | 3 |
| 3 | 88 - 131 | 2 |
| 4 | 132 - 175 | 0 |
| 5 | 176 - 219 | 2 |
| 6 | 220 - 263 | 2 |
| 7 | 264 - 307 | 0 |
| 8 | 308 - 351 | 0 |
| 9 | 352 - 395 | 1 |
| 10 | 396 - 439 | 0 |
| 11 | 440 - 483 | 1 |
| 12 | 484 - 527 | 0 |
| Sigma | Empirical formula | Range | Frequency | % |
|---|---|---|---|---|
| 1 sigma | mean - 1 * SD mean + 1 * SD | 55.8430 - 313.8490 | 8 | 66.7% |
| 2 sigma | mean - 2 * SD mean + 2 * SD | -73.1600 - 442.8520 | 11 | 91.7% |
| 3 sigma | mean - 3 * SD mean + 3 * SD | -202.1630 - 571.8550 | 12 | 100.0% |
68-95-99.7 rule states that in a typical normal distribution, 68% of the data points fall within +/- 1 standard deviation of the mean.
95% within 2 standard deviation from the mean Almost 100% within 3 standard deviations from the mean
Statistical Formulae
Formula to calculate Count
Count = n
where n is the total number of items in the dataset
Formula to calculate Sum
Sum = a1+a2+...+an
where, n is a1, a2, an, are data values
Formula to calculate Minimum
Min = 1/2 (r+s-|r-s|)
where, r is first number and s is second number
Formula to calculate Maximum
Max = 1/2 (r+s+|r-s|)
where, r is first number and s is second number
Formula to calculate Range
Range = max-min
where, max is maximum number and min is minimum number
Formula to calculate Mean
Mean = 1/n(a1+a2+...+an)
where, n is the number of observation and a1,a2,an are data values
Formula to calculate Median
Median = [(n + 1) / 2]th term
where, n is the number of observation
Formula to calculate Mode
Mode = L + (fm-f1)h /(fm-f1)+(fm-f2)
where, l is Lower limit Mode of modal class,fm is Frequency of modal class,f1 is Frequency of class preceding the modal class, f2 is Frequency of class succeeding the modal class,h is Size of class interval
Formula to calculate Quartile
Q1 = ((n+1)/4)
Q2 = ((n+1)/2)
Q3 = (3(n+1)/4)
where, q1 is first quartile, q2 is second quartile, q3 is third quartile and n is integer numbers
Formula to calculate Outlier
U = q3 + 1.5 (q3-q1)
L = q1 - 1.5 (q3-q1)
where, U is Upper Limit and L is Lower Limit and q1 is first quartile and q3 is third quartile
Formula to calculate Variance
S2 = 1 n - 1 ∑ i = 1 n ( x i - x ¯ ) 2
where, n is Number of observations in dataset, xi is ith observation in the sample and x ¯ is mean
Formula to calculate Standard Deviation
SD = 1 n - 1 ∑ i = Square root(1 n ( x i - x ¯ ) 2)
where, n is Number of observations in sample, xi is ith observation in the sample and x ¯ is Sample mean
Formula to calculate Standard Error
SE = SD/Square root(n)
where, SE is Standard Error, SD is standard deviation and n is total numbers
Formula to calculate Sample Variance
S2 = (1/ n - 1 ) * ∑ i( x i - x ¯ )
where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean
Formula to calculate Sample Standard Deviation
S = Square root((1/ n - 1 ) * ∑ i( x i - x ¯ ) 2)
where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean
Formula to calculate Sample Standard Error
SSE = SSD/Square root(n)
where, SSE is Sample Standard Error, SSD is sample standard deviation and n is total numbers
Formula to calculate Sigma
1 Sigma = Mean - 1 * Standard Deviation , Mean + 1 * Standard Deviation
2 Sigma = Mean - 2 * Standard Deviation , Mean + 2 * Standard Deviation
3 Sigma = Mean - 3 * Standard Deviation , Mean + 3 * Standard Deviation
Formula to calculate Class Interval Width
CIW = SD / 3
where, SD is standard deviation
