{"success":true,"version":"v1","request":{"tool":"list_calculators","category":"statistics"},"result":{"entity_type":"calculator_list","status":"completed","count":14,"calculators":[{"calculator_id":"descriptive-statistics","entity_type":"calculator","name":"Descriptive Statistics Calculator","category":"statistics","tool_name":"calculate_descriptive_statistics","description":"Computes summary statistics for a list of numbers: count, sum, mean, median, mode, range, sample and population variance and standard deviation, standard error, coefficient of variation, quartiles (linear interpolation) and skewness.","use_when":"You have a set of numeric observations and need its central tendency, spread or quartiles, e.g. the standard deviation of a data set.","do_not_use_when":"You need a single percentile or the percentile rank of one value (use percentile), a standardised score (use z-score), or statistics of two paired variables (use correlation or linear-regression).","required_inputs":["values"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/descriptive-statistics","markdown":"https://tttkmbb.com/statistics/descriptive-statistics.md","schema":"https://tttkmbb.com/api/v1/calculators/descriptive-statistics","api":"https://tttkmbb.com/api/v1/calculate/descriptive-statistics"}},{"calculator_id":"z-score","entity_type":"calculator","name":"Z-Score Calculator","category":"statistics","tool_name":"calculate_z_score","description":"Standardises a value against a mean and standard deviation (z = (x − μ) / σ) and reports the corresponding percentile and tail probabilities under the normal distribution.","use_when":"You need how many standard deviations a value lies from the mean, or the percentile a value corresponds to in a normally distributed population (test scores, measurements, quality control).","do_not_use_when":"You need the probability between two values or the density (use normal-distribution), the data are clearly not normal, or you need the empirical percentile rank within an actual data set (use percentile).","required_inputs":["value","mean","std_dev"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/z-score","markdown":"https://tttkmbb.com/statistics/z-score.md","schema":"https://tttkmbb.com/api/v1/calculators/z-score","api":"https://tttkmbb.com/api/v1/calculate/z-score"}},{"calculator_id":"normal-distribution","entity_type":"calculator","name":"Normal Distribution Calculator","category":"statistics","tool_name":"calculate_normal_distribution_probability","description":"Computes cumulative probabilities P(X < x), P(X > x) and P(x < X < x2) and the density for a normal (Gaussian) distribution with a given mean and standard deviation.","use_when":"You need the probability that a normally distributed quantity falls below, above or between given values, or the z-scores of those values.","do_not_use_when":"The variable is a count of successes or events (use binomial-distribution or poisson-distribution), or you need the value at a given probability from real data (use percentile).","required_inputs":["x"],"optional_inputs":["mean","std_dev","x2"],"urls":{"html":"https://tttkmbb.com/statistics/normal-distribution","markdown":"https://tttkmbb.com/statistics/normal-distribution.md","schema":"https://tttkmbb.com/api/v1/calculators/normal-distribution","api":"https://tttkmbb.com/api/v1/calculate/normal-distribution"}},{"calculator_id":"confidence-interval","entity_type":"calculator","name":"Confidence Interval Calculator","category":"statistics","tool_name":"calculate_confidence_interval","description":"Computes a confidence interval for a population mean from the sample mean, standard deviation and sample size using the normal (z) critical value: mean ± z · s / √n.","use_when":"You have a sample mean, its standard deviation and the sample size and want the interval that likely contains the population mean at a given confidence level.","do_not_use_when":"The statistic is a proportion or survey percentage (use margin-of-error), or the sample is small (n < 30) with an unknown population SD, where a t-based interval is the correct choice and this z interval is slightly too narrow.","required_inputs":["sample_mean","std_dev","sample_size"],"optional_inputs":["confidence_level_percent"],"urls":{"html":"https://tttkmbb.com/statistics/confidence-interval","markdown":"https://tttkmbb.com/statistics/confidence-interval.md","schema":"https://tttkmbb.com/api/v1/calculators/confidence-interval","api":"https://tttkmbb.com/api/v1/calculate/confidence-interval"}},{"calculator_id":"sample-size","entity_type":"calculator","name":"Sample Size Calculator","category":"statistics","tool_name":"calculate_sample_size","description":"Computes the number of respondents needed to estimate a population proportion within a given margin of error at a given confidence level (Cochran's formula), with an optional finite population correction.","use_when":"You are planning a survey, poll or A/B test on a proportion and need to know how many people to sample for a target margin of error.","do_not_use_when":"You already have a sample and want its margin of error (use margin-of-error), or you are estimating a mean rather than a proportion (the formula would need the standard deviation instead of p(1 − p)).","required_inputs":["margin_of_error_percent"],"optional_inputs":["confidence_level_percent","expected_proportion_percent","population_size"],"urls":{"html":"https://tttkmbb.com/statistics/sample-size","markdown":"https://tttkmbb.com/statistics/sample-size.md","schema":"https://tttkmbb.com/api/v1/calculators/sample-size","api":"https://tttkmbb.com/api/v1/calculate/sample-size"}},{"calculator_id":"margin-of-error","entity_type":"calculator","name":"Margin of Error Calculator","category":"statistics","tool_name":"calculate_margin_of_error","description":"Computes the margin of error (half-width of the confidence interval) of a sample proportion from the sample size, confidence level and observed percentage, with an optional finite population correction.","use_when":"You have poll or survey results (n respondents, x % answering a certain way) and need the ± margin at a confidence level.","do_not_use_when":"You are still planning the survey and need the required sample size (use sample-size), or the statistic is a mean rather than a percentage (use confidence-interval).","required_inputs":["sample_size"],"optional_inputs":["confidence_level_percent","proportion_percent","population_size"],"urls":{"html":"https://tttkmbb.com/statistics/margin-of-error","markdown":"https://tttkmbb.com/statistics/margin-of-error.md","schema":"https://tttkmbb.com/api/v1/calculators/margin-of-error","api":"https://tttkmbb.com/api/v1/calculate/margin-of-error"}},{"calculator_id":"binomial-distribution","entity_type":"calculator","name":"Binomial Distribution Calculator","category":"statistics","tool_name":"calculate_binomial_probability","description":"Computes the probability of exactly, at most, at least, fewer than or more than k successes in n independent trials with success probability p, plus the mean, variance and standard deviation of the distribution.","use_when":"You have a fixed number of independent yes/no trials with a constant success probability (coin flips, defect counts in a batch, conversions among n visitors) and need the probability of a number of successes.","do_not_use_when":"Trials are not independent or p changes, the number of trials is not fixed, or you count events over time or space at an average rate (use poisson-distribution).","required_inputs":["trials","successes","probability_of_success"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/binomial-distribution","markdown":"https://tttkmbb.com/statistics/binomial-distribution.md","schema":"https://tttkmbb.com/api/v1/calculators/binomial-distribution","api":"https://tttkmbb.com/api/v1/calculate/binomial-distribution"}},{"calculator_id":"poisson-distribution","entity_type":"calculator","name":"Poisson Distribution Calculator","category":"statistics","tool_name":"calculate_poisson_probability","description":"Computes the probability of exactly, at most, at least, fewer than or more than k events when events occur independently at a constant average rate λ per interval, plus the mean, variance and standard deviation.","use_when":"You count independent events over a fixed interval of time or space with a known average rate (calls per hour, defects per metre, arrivals per minute) and need the probability of a given count.","do_not_use_when":"The number of trials is fixed and each has a success probability (use binomial-distribution), the rate varies over the interval, or events cluster (over-dispersion).","required_inputs":["lambda","events"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/poisson-distribution","markdown":"https://tttkmbb.com/statistics/poisson-distribution.md","schema":"https://tttkmbb.com/api/v1/calculators/poisson-distribution","api":"https://tttkmbb.com/api/v1/calculate/poisson-distribution"}},{"calculator_id":"probability-of-events","entity_type":"calculator","name":"Probability of Two Events Calculator","category":"statistics","tool_name":"calculate_event_probabilities","description":"Combines the probabilities of two events A and B that are either independent or mutually exclusive into the probabilities of both, at least one, exactly one, one but not the other, and neither occurring.","use_when":"You know P(A) and P(B) and how the events relate (independent or mutually exclusive) and need P(A and B), P(A or B), P(neither) or P(exactly one).","do_not_use_when":"The events are dependent with a known conditional probability (apply P(A and B) = P(A)·P(B|A) directly), you need the probability of k successes in repeated trials (use binomial-distribution), or you need an expected payoff (use expected-value).","required_inputs":["probability_a","probability_b"],"optional_inputs":["relationship"],"urls":{"html":"https://tttkmbb.com/statistics/probability-of-events","markdown":"https://tttkmbb.com/statistics/probability-of-events.md","schema":"https://tttkmbb.com/api/v1/calculators/probability-of-events","api":"https://tttkmbb.com/api/v1/calculate/probability-of-events"}},{"calculator_id":"correlation","entity_type":"calculator","name":"Correlation Coefficient Calculator","category":"statistics","tool_name":"calculate_correlation","description":"Computes the Pearson product-moment correlation coefficient r, the coefficient of determination r², and the sample covariance for two paired lists of numbers, with a strength/direction interpretation.","use_when":"You have paired measurements of two numeric variables and want to quantify the strength and direction of their linear relationship.","do_not_use_when":"You need the fitted line or predictions (use linear-regression), the relationship is clearly non-linear or the data are ranks/ordinal (Spearman's rank correlation is more appropriate), or you only have one variable (use descriptive-statistics).","required_inputs":["x_values","y_values"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/correlation","markdown":"https://tttkmbb.com/statistics/correlation.md","schema":"https://tttkmbb.com/api/v1/calculators/correlation","api":"https://tttkmbb.com/api/v1/calculate/correlation"}},{"calculator_id":"linear-regression","entity_type":"calculator","name":"Linear Regression Calculator","category":"statistics","tool_name":"calculate_linear_regression","description":"Fits an ordinary least-squares line to paired (x, y) data and returns the slope, intercept, equation, Pearson r, R², the standard error of the estimate and an optional prediction for a new x.","use_when":"You want the best-fit straight line through paired data, its equation, or a predicted y for a given x (trend lines, calibration curves, simple forecasting).","do_not_use_when":"The relationship is curved or has several predictors (needs polynomial or multiple regression), or you only need the strength of association (use correlation).","required_inputs":["x_values","y_values"],"optional_inputs":["x_new"],"urls":{"html":"https://tttkmbb.com/statistics/linear-regression","markdown":"https://tttkmbb.com/statistics/linear-regression.md","schema":"https://tttkmbb.com/api/v1/calculators/linear-regression","api":"https://tttkmbb.com/api/v1/calculate/linear-regression"}},{"calculator_id":"weighted-average","entity_type":"calculator","name":"Weighted Average Calculator","category":"statistics","tool_name":"calculate_weighted_average","description":"Computes the weighted arithmetic mean Σ(w·x) / Σw of a list of values and a matching list of weights, along with the total weight and the unweighted mean for comparison.","use_when":"Values contribute unequally to an average: course grades with credit weights, portfolio returns by allocation, survey answers with sampling weights, average price over different quantities.","do_not_use_when":"All items count equally (use descriptive-statistics for the plain mean), or the weights are probabilities of outcomes (use expected-value, which also gives the variance).","required_inputs":["values","weights"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/weighted-average","markdown":"https://tttkmbb.com/statistics/weighted-average.md","schema":"https://tttkmbb.com/api/v1/calculators/weighted-average","api":"https://tttkmbb.com/api/v1/calculate/weighted-average"}},{"calculator_id":"percentile","entity_type":"calculator","name":"Percentile Calculator","category":"statistics","tool_name":"calculate_percentile","description":"For a list of numbers, computes the value at a given percentile (linear interpolation, as in Excel PERCENTILE.INC) and/or the percentile rank of a given value (percentage of values below it, counting ties as half).","use_when":"You need the k-th percentile of a data set (e.g. the 90th percentile response time) or want to know what percentile a particular value falls at within the data.","do_not_use_when":"You want a percentile from a normal distribution rather than actual data (use z-score or normal-distribution), or you need quartiles together with other summary statistics (use descriptive-statistics).","required_inputs":["values"],"optional_inputs":["percentile","value"],"urls":{"html":"https://tttkmbb.com/statistics/percentile","markdown":"https://tttkmbb.com/statistics/percentile.md","schema":"https://tttkmbb.com/api/v1/calculators/percentile","api":"https://tttkmbb.com/api/v1/calculate/percentile"}},{"calculator_id":"expected-value","entity_type":"calculator","name":"Expected Value Calculator","category":"statistics","tool_name":"calculate_expected_value","description":"Computes the expected value E[X] = Σ x·p(x), the variance and the standard deviation of a discrete random variable from its list of outcomes and their probabilities.","use_when":"You have a set of possible outcomes (payoffs, scores, counts) with known probabilities and need the long-run average and its spread: bets, lotteries, insurance, decision analysis.","do_not_use_when":"The probabilities are unknown and you have observed data instead (use descriptive-statistics), or the weights are not probabilities (use weighted-average).","required_inputs":["values","probabilities"],"optional_inputs":[],"urls":{"html":"https://tttkmbb.com/statistics/expected-value","markdown":"https://tttkmbb.com/statistics/expected-value.md","schema":"https://tttkmbb.com/api/v1/calculators/expected-value","api":"https://tttkmbb.com/api/v1/calculate/expected-value"}}]},"timestamp":"2026-09-23T23:26:40Z","next_actions":[],"links":{"docs":"https://tttkmbb.com/calculators.md"}}