1-Var Stats

Mean, standard deviation, five-number summary, and more from a list of data, just like STAT → CALC → 1-Var Stats.

Inputs

Your data is

Paste or type numbers separated by commas, spaces, or new lines. A column copied from Excel or Google Sheets works too.

Results update as you type.

Results

x̄ = 24.2  ·  Sx = 6.689  ·  n = 15

The 15 values have a mean of 24.2 and a sample standard deviation of 6.689; a typical value is about 6.689 away from the mean.

Modified boxplot of the data. The box runs from Q1 = 19 to Q3 = 27 with the median at 22. Whiskers reach 18 and 35. Outlier plotted as separate dots: 41.2025303540

Results

x̄ (mean)24.2
Σx363
Σx²9411
Sx (sample SD)6.689
σx (population SD)6.4622
s² (sample variance)44.7429
n15
minX18
Q119
Med22
Q327
maxX41
Range23
IQR8
Mode18, 19, 20

On the TI-84

Enter the data in L1 (STAT → 1:Edit). Then STAT → CALC → 1:1-Var Stats, List: L1, FreqList blank.

1-Var Stats L1

Show steps
  1. Mean. x̄ = Σx ÷ n = 363 ÷ 15 = 24.2
  2. Sample standard deviation. Add up the squared deviations from the mean: Σ(x − x̄)² = 626.4. Then s² = 626.4 ÷ (15 − 1) = 44.7429 and s = √44.7429 = 6.689.
  3. Order the data. 18, 18, 19, 19, 20, 20, 21, 22, 23, 24, 26, 27, 30, 35, 41
  4. Median. n = 15 is odd, so the median is the middle value: Med = 22.
  5. Quartiles. Q1 is the median of the lower half and Q3 is the median of the upper half (the median itself is left out of both halves): Q1 = 19, Q3 = 27.

About this calculator

When to use this

Use 1-Var Stats any time you have one list of numbers and want to describe it: the center (mean and median), the spread (standard deviation, range, IQR), and the five-number summary. It gives the same numbers, in the same order, as the TI-84's 1-Var Stats screen.

Reading the output

About the quartiles

Quartiles are found the way the TI-84 does it: Q1 is the median of the lower half and Q3 is the median of the upper half, leaving out the median when n is odd. Other software may give slightly different quartiles.