Name: _________________________________________ Date: _________________ Pd: _____
Section 3-4
Percentiles, Quartiles and Deciles – Measures of Position
percentile –
Formula to find Percentile:
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 =
(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 ≤ 𝑋)
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠
Formula to Find Position of a Given Percentile
𝑖=
𝑛∙𝑝
100
Example: Finding the Percentile of a Value in a Data Set
A teacher gives a 50-point test to 10 students. The scores are shown below. Find the percentile
rank of 36.
18, 36, 45, 40, 30, 38, 48, 27, 39, 25
Step 1: Arrange the data in order from lowest to highest.
Step 2: Substitute in the formula.
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 =
(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 ≤ 𝑋)
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠
Step 3: Calculate the percentile.
Example: Finding the Value the Corresponds to a Percentile (when i is a
decimal)
Using the data from the previous example, find the value corresponding to the 25th percentile.
Step 1: Arrange the data in order from lowest to highest.
Step 2: Substitute in the formula
𝑖=
𝑛∙𝑝
100
Step 3: If i is not a whole number, round it up to the next whole number. (If i is a whole
number, see the next example.) Start at the lowest value and count over to the ith value. This is
the value that corresponds to the 25th percentile.
Example: Finding the Value the Corresponds to a Percentile (when i is a
decimal)
Using the data from the previous example, find the value that corresponds to the 60th percentile.
Step 1: Arrange the data in order from smallest to largest.
Step 2: Substitute in the formula
𝑖=
𝑛∙𝑝
100
Step 3: If i is a whole number, use the value halfway between the i and the i + 1 value when
counting up from the lowest value.
quartile –
25%
25%
25%
25%
Note: To find Q1, simply calculate the 25th percentile of the data. To find Q3, simply calculate
the 75th percentile of the data. To find Q2, find the median of the data.
Example: Finding Quartiles
Find Q1, Q2, and Q3 for the data set 10, 2, 9, 15, 23, 30, 8, 17, 25, 28
Step 1: Arrange the data in order.
Step 2: Find the median (Q2).
Step 3: Find the 25th percentile (Q1) and the 75th percentile (Q3) using the formula
𝑖=
𝑛∙𝑝
100
Decile –
Note: Deciles are denoted by D1, D2, D3, …, D9 and the correspond to P10, P20, P30, …, P90.
Deciles can be found using the formulas given for percentiles.