The Observational Statistics calculator computes the most common observational statistics for columns in a table of data.
INSTRUCTIONS: Enter the following:
- (x) Numeric Observations. Enter rows of comma separated numeric values e.g. 4,-1.2,8,9 . To do so, click on the field and
- enter the data manual, or
- use cut / copy / paste, or
- upload a csv with a uniform table of real numbers.
- (c) Column Number.
STATISTICS: The calculator returns the descriptive statistics below for the identified column.
- count - number (n) of values in the column.
- min - minimum value
- max - maximum value
- sum(Σx) - sum of the values in a set.
- Σx² - sum of the squared values
- (Σx)² - square of the summed values.
- mean - mean (average) of values
- median - middle ordered value
- mid point - mid point of value range
- mode - most frequent observation
- range - difference between the max and the min.
- MAD - Mean Absolute Deviation
- SDOM - Standard Deviation of Mean
- sort up - values in ascending order.
- sort down - values in descending order.
- var-pop - population variance of the values
- sd-pop - population standard deviation of the values
- var-sample - sample variance of the values
- sd-sample - sample standard deviation of the values
How to Enter Data
Enter the data in comma separated values with a new line for each record. Note: it is important to be consistent with number of columns when manually entering the data.
One can also upload a CSV (comma separated values) file from your device into this calculator by clicking on the
.
button.
Example
Enter the following tabular data and choose a column between 1 and 4:
-56,347,356,147
326,-116,386,-276
23,309,-230,-109
390,49,385,405
-87,289,32,33
-210,382,244,5
-85,206,386,44
318,-294,-16,-294
357,-152,-154,147
482,-16,-241,-191
-85,281,267,280
254,364,352,72
-32,-322,-90,-385
460,434,-89,461
23,49,-243,-42
128,-228,-137,-61
370,-75,32,-287
306,-387,51,33
-23,-282,467,271
You will see the observational statistics for that column.
This calculator is a prominent feature with other statistical functions in the College Level Statistics Calculator (Stat Calc).
Statistics Calculators
- Observational Stats: This function accepts a table of numbers separated by commas and calculates observational statistics for any of the columns. This includes count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.
- Frequency Distribution: This function lets you enter a string of numbers separated by commas, a low and high range and a number of bins. It then computes how many of the observations are in each of the bins between the high and low values designated.
- Paired Sample t-test: This computes the various parameters associated with the Paired Sample t-test.
- ANOVA (one way): The is one way analysis of variance
- (χ2) Chi-Square Test: This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.
- Linear Regression: This computes the regression line (least-squares) through a set of X and Y observations. It also computes the regression coefficient (r).
- y = a + bx: This is linear equation used with Linear Regression to predict values of Y.
- Wilcoxon Signed Rank Test: This provides the Wilcoxon statistics and critical value for two groups of numeric observations based on an alpha value and whether it's a one or two tailed test.
- Slope-Intercept form of a Line based on two points.
- Slope between two points
- Range value based on the slope-intercept formula of a line and a value of the domain.
- Compute the Probability between z SCORES
- College Level Statistics Calculator (Stat Calc).
- Count of Observations in a Set - this is the number (n) of values in a set.
- Minimum Value in a Set - this is the minimum observed value
- Maximum Value in a Set- this is the maximum value in the set.
- Numeric Sort (up and down) - this returns a comma separated list of the observations in ascending or descending order.
- Create a random subset of the a list of numeric values
- Random number from a range you specify
- Frequency distribution of data.
- Σx - this is the sum of the values in a set.
- Σx² - this is the sum of the squared values
- (Σx)² - this is the square of the summed values.
- Mean - the is the mean (average) of the observed values
- Median - the middle ordered value
- Mode - the most recurring observation
- Mid Point in a Set - this is the mid point of the observation range.
- Range in a Set - this is the difference between the max and the min.
- Population Variance of the values
- Population standard deviation of the values
- Sample Variance of the values
- Sample Standard Deviation of the values
- Compute the z SCORE based on the mean and standard deviation
- Compute the z SCORE in a set of observations
- Compute the percentile of a single observation (y) in a set (X)
- SDOM - standard deviation of mean
- Percent Relative Standard Deviation
Thanks to Dr. Lee Hammerstrom, professor of math stats at Eastern Nazarene College, for his advice and testing.
The Math
The formulas for the statistics are as follows:
sum
`S = sum(x)`
sum of squares
Σx²`= sum(x^2)`
square of the sum
(Σx)² = `(sum(x))^2`
averages
- mean: `mu = (sum(x))/n` where n is the number of observations
- median: middle value if in an odd number of observations. If there is an even number of observations, it's the average of the two middle values.
- mid-point: `mp = (min + max)/2`
variance
- Population Variance: `sigma^2 = (sum_1^n(x_n-mu)^2)/n`
- Sample Variance: `sigma^2 = (sum_1^n(x_n-mu)^2)/(n-1)`
standard deviation
- Population Standard Deviation: `sigma = sqrt((sum_1^n(x_n-mu)^2)/n)`
- Sample Standard Deviation: `sigma = sqrt((sum_1^n(x_n-mu)^2)/(n-1))`
Mean Absolute Deviation
- MAD = `1/n sum_(i=1)^n | x_i - barx |`
Statistics Calculators
- Stats Calc - Complete set of entry level college statistics functions
- Simple Stats - Complete set of Observational statistics for a set of data
- Linear Regression - Least-squares trend line for a set of data
- One Way ANOVA - One way Analysis of Variance for three sets of data
Growth Calculators
- Logistic Growth
- Malthusian Growth Model
- Organism Count (Logistic Growth)
- Max Potential Growth Rate (biotic potential)
- How Many Ancestors
- Simple Stats Calc - Simple observation statistics (see below)
- Math Statistics Calc - College level statistics and regression calculator.
Statistics in Culture
"There are three kinds of lies: lies, damn lies and statistics." Mark Twain