Calculators

Statistics

Calculator Use

Generate an online stem and leaf plot, or stemplot, and calculate basic descriptive statistics for a sample data set with 4 or more values and up to 2500 values, positive and negative. Enter values separated by commas such as 31, 26, 20, 28, 13, 10, 18, 13.

You can also copy and paste lines of data points from documents such as Excel spreadsheets or text documents with or without commas in the formats shown in the table below.

Notes:

• Does not handle decimals. If you need to work with decimals you can multiply all of your values by a factor of 10 and calculate based on those.  You will just need to interpret the results appropriately.

For additional descriptive statistical values see Descriptive Statistics Calculator.

Below is a sample stem and leaf plot and calculated statistical values.

Sample Stem and Leaf Plot with Split Stems

Data Set:

42, 14, 22, 16, 2, 15, 8, 27, 6, 15, 19, 48, 4, 31, 26, 20, 28, 13, 10, 18, 13, 15, 48, 16, 15, 5, 18, 16, 28, 11, 0, 27, 28, 5, 40, 21, 18, 7, 12, 6, 40, 12, 2, 20, 35, 3, 16, 13, 8, 15, 7, 65, 65, 25, 15, 21, 12, 12, 35, 30, 14, 35, 20, 35, 7, 35

Stem and Leaf Plot:

Basic Statistics Formulas and Calculations used in this Calculator

Minimum

Ordering a data set {x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n} from lowest to highest value, the minimum is the smallest value x₁.

\[ \text{Min} = x_1 = \text{min}(x_i)_{i=1}^{n} \]

Maximum

Ordering a data set {x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n} from lowest to highest value, the maximum is the largest value x_n.

\[ \text{Max} = x_n = \text{max}(x_i)_{i=1}^{n} \]

Sum

The sum is the total of all data values. {x₁ + x₂ + x₃ + ... + x_n}

\[ \text{Sum} = \sum_{i=1}^{n}x_i \]

Size

The total number of data values in a data set.

\[ \text{Size} = n = \text{count}(x_i)_{i=1}^{n} \]

Mean

The sum of all of the data divided by the size. The mean is also known as the average.

\[ \overline{x} = \dfrac{\sum_{i=1}^{n}x_i}{n} \]

Median

Ordering a data set {x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n} from lowest to highest value, the median is the numeric value separating the upper half of the ordered sample data from the lower half. If n is odd the median is the center value. If n is even the median is the average of the 2 center values.

If n is odd the median is the value at position p where

\[ p = \dfrac{n + 1}{2} \] \[ \widetilde{x} = x_p \]

If n is even the median is the average of the values at positions p and p + 1 where

\[ p = \dfrac{n}{2} \] \[ \widetilde{x} = \dfrac{x_{p} + x_{p+1}}{2} \]

Mode

The value or values that occur most frequently in the data set.

Standard Deviation

\[ s = \sqrt{\dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n - 1}} \]

Variance

\[ s^{2} = \dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n - 1} \]