Q.Define quartiles, deciles and percentiles. Into how many parts does each divide a series, and how many such partition values does each family give?

The three families of partition values differ only in how many equal parts they split a series into.

Quartiles divide an ordered series into 4 equal parts, giving 3 quartiles — Q1 (lower), Q2 (middle, = median), Q3 (upper).

Deciles divide an ordered series into 10 equal parts, giving 9 deciles — D1 through D9.

Percentiles divide an ordered series into 100 equal parts, giving 99 percentiles — P1 through P99.

In every case, the number of partition VALUES is always one less than the number of PARTS the series is divided into (dividing a line into 4 pieces needs only 3 cut points, and so on).

Saying quartiles give '4 values' instead of 3 — dividing a series into N equal parts always requires exactly N−1 partition points, not N.