Ex:           A company manufacturing inexpensive analog function generators measures the frequency they produce when set to 1 kHz. They measure the following values in Hz:

        f1 = 998       f2 = 997       f3 = 1003     f4 = 1001     f5 = 999       f6 = 1001

        f7 = 998       f8 = 1002     f9 = 1000     f10 = 1001   f11 = 1000

Make a quantile plot of the data.

Sol'n:      The quantile plot shows what fraction of data values are less than a given data value. After the data are ordered from lowest to highest, the values are assigned sequential numbers, i:

997,   998,  998,   999,   1000,   1000,   1001,  1001,  1001,  1002,         1003

i = 1       2       3       4        5         6         7         8         9       10     11

Given the total number of data points, n = 11, we use the following formula that produces the quantile value, qi:

The offsets in the numerator and denominator are adjustments for the use of discrete integer values. Note that if i = 1 and n = 1, the quantile would be 5/8 over 5/4, implying that half the data is less than the single data point.