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Data Set Analyzer

Solve data set problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

Mean = Sum/n, Variance = Sum((xi - mean)^2)/n, StdDev = sqrt(Variance)

Descriptive statistics summarize data through central tendency (mean, median, mode), dispersion (range, variance, standard deviation, IQR), and shape (skewness, kurtosis). The 95% confidence interval uses CI = mean +/- 1.96 * SEM where SEM = sample_std_dev / sqrt(n).

Worked Examples

Example 1: Student Test Scores Analysis

Problem:Analyze the following test scores: 72, 85, 90, 68, 95, 78, 88, 92, 76, 84. Find mean, median, standard deviation, and 95% confidence interval.

Solution:Sorted: 68, 72, 76, 78, 84, 85, 88, 90, 92, 95\nSum = 828, Count = 10\nMean = 828/10 = 82.8\nMedian = (84 + 85)/2 = 84.5\nVariance = [(72-82.8)^2 + ... + (84-82.8)^2]/10 = 68.56\nStd Dev = sqrt(68.56) = 8.28\nSample Std Dev = sqrt(68.56 * 10/9) = 8.73\nSEM = 8.73/sqrt(10) = 2.76\n95% CI = 82.8 +/- 1.96*2.76 = [77.39, 88.21]

Result:Mean: 82.8 | Median: 84.5 | Std Dev: 8.28 | 95% CI: [77.39, 88.21]

Example 2: Sales Data Distribution

Problem:Analyze daily sales figures: 150, 200, 175, 225, 180, 300, 190, 210, 195, 185, 205, 170.

Solution:Sorted: 150, 170, 175, 180, 185, 190, 195, 200, 205, 210, 225, 300\nCount = 12, Sum = 2385\nMean = 198.75\nMedian = (190+195)/2 = 192.5\nRange = 300-150 = 150\nQ1 = 176.25, Q3 = 208.75\nIQR = 32.5\nSkewness = 1.24 (right-skewed due to $300 outlier)\nThe $300 value exceeds Q3 + 1.5*IQR = 257.5, flagged as outlier

Result:Mean: 198.75 | Median: 192.5 | IQR: 32.5 | Skewness: 1.24 (right-skewed)

Frequently Asked Questions

What is a data set analyzer and what statistics does it calculate?

A data set analyzer is a statistical tool that computes descriptive statistics from a collection of numerical values. It calculates measures of central tendency including the mean (arithmetic average), median (middle value), and mode (most frequent value). It also computes measures of dispersion such as range, variance, standard deviation, and interquartile range. Advanced metrics include skewness which measures asymmetry of the distribution, kurtosis which measures tail heaviness, coefficient of variation for comparing variability across different scales, and the standard error of the mean used for constructing confidence intervals. These statistics provide a comprehensive numerical summary of your data set.

Is my data stored or sent to a server?

No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.

References

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy