Statistics • Numerical Descriptive Measures
Enter a set of ungrouped data (individual values). This tool ranks the data, finds the quartiles \(Q_1, Q_2, Q_3\), the interquartile range \(\text{IQR} = Q_3 - Q_1\), an optional percentile \(P_k\), and the percentile rank of a value \(x_r\). The diagrams show a bar cut into 4 equal parts (quartiles) and a 0–100% scale for percentiles.
It first ranks the data from smallest to largest. Q2 is the median of all values, then Q1 is the median of the lower half and Q3 is the median of the upper half, omitting the overall median from both halves when n is odd.
The interquartile range measures the spread of the middle 50% of the data. It is calculated as IQR = Q3 - Q1.
It uses an approximate ranked position: position = (k x n) / 100 in the ordered list. The position is rounded to the nearest whole number and the value at that rank is reported as Pk.
Percentile rank is the percentage of data values that are less than xr. It is computed as (number of values less than xr / n) x 100.
Different sources use different rules for handling halves and positions, especially when n is odd or when the percentile position is not an integer. This calculator follows a specific ranking and rounding rule shown in the step-by-step explanation.