x barStatistics · Data handling
Statistics Calculator with the full table
Paste your data or a frequency table. Get the mean, median, mode, standard deviation and quartiles — with the working table your teacher expects.
- Free steps
- Graph
- Checked answers
0 values · separate with commas, spaces or new lines — or paste a column from Excel / Google Sheets.
Try it
Drag the data. Find the balance point.
The mean is where the dot plot balances; the box plot shows the middle half. Drag one dot far to the right: the mean chases it, the median and quartiles hardly move, and the 1.5 × IQR rule flags it as an outlier.
Balance rule
∑ (x - x bar) = 0The mean is pulled right of the median — the data are skewed right.
Quartiles here: median of each half, middle value left out (TI-84 / AP). The calculator above lets you pick other textbook methods.
Drag a dot, or focus it (Tab) and use ← → (Page Up/Down for 5). Switch to the histogram to see the same data in bars.
Why this statistics calculator is different
01
Every formula, every row
See x bar = (∑ x)/(n) worked out, plus a deviations table behind both the population σ and the sample s standard deviation, side by side.
02
Grouped data, CBSE and GCSE
Class intervals give the estimated mean three ways, the modal class (by frequency density for unequal widths), and the median and quartiles by interpolation.
03
Quartiles you can trust
The quartile method is named in every answer, four textbook conventions are compared, and outliers are flagged with the 1.5 × IQR rule on a box plot.
What does a statistics calculator do?
A statistics calculator summarises a data set with a few numbers: a centre (mean, median, mode) and a spread (range, interquartile range, variance and standard deviation). Paste your numbers and each one is worked out with its formula and a working table, so you can check your own answer line by line.
The mean x bar = (∑ x)/(n) is the balance point of the data; the median is the middle value once the data are sorted; the mode is the most common value. The standard deviation measures the typical distance from the mean: divide by n for a whole population, or by n - 1 for a sample.
These ideas run through school maths — grouped data in CBSE Class 10, cumulative frequency and box plots at GCSE, standard deviation in AP Statistics and IB. Raw lists, frequency tables, two-row textbook tables and grouped classes are all handled.
How to use the statistics calculator
- 1Type or paste your numbers — commas, spaces, tabs and new lines all work, so a column from Excel or Google Sheets is fine. Headers and words such as “find the mean of” are ignored.
- 2For a frequency table type `1:4, 2:7, 3:5` or paste the rows `x: 1 2 3` and `f: 4 7 5`. For grouped data type `0-10:5, 10-20:8` or the GCSE form `0 < t ≤ 10: 4`.
- 3Pick the quartile method your textbook uses, then press Solve.
- 4Read the summary card and the steps. The Table tab has the deviations table, the five-number summary and the quartiles by every method; Graph shows the histogram and box plot (or ogives for grouped data).
Statistics calculator formulas: mean, median, SD and quartiles
Mean (the average)
Add the values and divide by how many there are; for a frequency table multiply each value by its frequency first.
Median and mode
Sort the data first; with an even number of values take the mean of the middle two. Data can have one mode, two modes or none.
Standard deviation: population and sample
The shortcut σ^2 = (∑ x^2)/(n) - x bar^2 gives the same variance and is used as a check.
Quartiles, IQR and outliers
Quartile conventions differ, so the method is named with every answer. Values outside the fences are outliers, drawn as separate points on the box plot.
Estimated mean of grouped data
x_i are class midpoints, a an assumed mean and h the class width. It is an estimate: each value is treated as if it sat at its class midpoint.
Median, quartiles and modal class of grouped data
l is the lower class boundary and cf the cumulative frequency before the class; Q_1 and Q_3 use n/4 and 3n/4. With unequal widths the modal class has the highest frequency density.
Statistics calculator worked example: mean, median, mode and SD
- 01
There are n = 8 values, already in order, with total ∑ x = 40.
x bar = 40/8 = 5 - 02
The 4th and 5th values are 4 and 5, so the median is their mean. The value 4 appears three times, so it is the mode.
Median = (4 + 5)/(2) = 4.5, Mode = 4 - 03
Square each deviation from the mean and add them: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16.
∑ (x - x bar)^2 = 32 - 04
Divide by n = 8 for the population variance, or by n - 1 = 7 for the sample variance, then take square roots.
σ^2 = 32/8 = 4 ⇒ σ = 2, s^2 = 32/7 ⇒ s ≈ 2.138 - 05
Quartiles (median of each half): Q_1 = 4 and Q_3 = 6. The fences are 1 and 9, so there are no outliers.
IQR = 6 - 4 = 2
Common statistics mistakes
Finding the median without sorting
The median of 7, 2, 9 is 7, not 2 — sort the data to 2, 7, 9 first.
Mixing up population and sample SD
Population standard deviation divides by n; sample standard deviation divides by n - 1. If the data are a sample, use s.
Using class limits instead of boundaries
For classes 10–19, 20–29 the formulas need the boundaries 9.5–19.5, 19.5–29.5. The calculator converts them and shows the step.
Picking the modal class by frequency when widths differ
With unequal class widths compare frequency densities (f ÷ width), not frequencies — and plot frequency density on the histogram.
Statistics calculator FAQ
What is the difference between population and sample standard deviation?+
Population standard deviation σ divides the sum of squared deviations by n and is used when you have every member of the group. Sample standard deviation s divides by n - 1, because a sample tends to underestimate the spread. Both are always shown, with the deviations table.
Why does my calculator give different quartiles?+
There is no single agreed rule. Graphing calculators and AP Statistics take the median of each half without the middle value; GCSE uses positions (n+1)/(4) and (3(n+1))/(4); spreadsheets interpolate. Small data sets give slightly different answers, so the method used is named and all four are compared in a table.
How do you find the mean from a grouped frequency table?+
Multiply each class midpoint by its frequency, add the products and divide by the total frequency: x bar ≈ (∑ f x)/(∑ f). It is an estimate because the exact values inside each class are unknown. The assumed-mean and step-deviation methods give the same answer with smaller numbers.
How do you find the median of grouped data?+
Work out n/2, find the first class whose cumulative frequency is greater than it, and interpolate: Median = l + (n/2 - cf)/(f) × h. The quartiles work the same way with n/4 and 3n/4 — what you would read off a cumulative frequency graph.
How do you identify outliers?+
Use the 1.5 × IQR rule: any value below Q_1 - 1.5 IQR or above Q_3 + 1.5 IQR is an outlier. In 10, 12, 13, 13, 14, 15, 16, 60 the upper fence is about 20, so 60 is flagged and drawn as a separate point on the box plot.
Can I paste data from Excel or Google Sheets?+
Yes. Copy a column or a row and paste it into the box; tabs, new lines, commas and semicolons all count as separators; headers such as “Score” are ignored. Two pasted columns of classes and frequencies are read as a grouped frequency table automatically.
How do I know the answers are right?+
Each result is recomputed by an independent route before Verified appears: the variance by two different formulas, the mean by a one-pass method, the median by counting, the grouped mean by three methods and the grouped median and quartiles from the ogive.
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