Measure of Position for Ungrouped Data

​

​Calculating Measures of Position: Interpolation

​When to Interpolate?

​Use interpolation when the position isn't a whole number. This ensures accuracy.

Interpolation Formula

Value = Lower Value + (Position - Lower Position) x (Upper Value - Lower Value)

Example

P₂₅ Position = 6.25. If the 6th value is 20 and the 7th value is 24, then
P₂₅ = 20 + (6.25 - 6) x (24 - 20)
P₂₅ = 20 + (0.25) x (4)
P₂₅ = 20 + 1 = 21, So P₂₅ = 21

​Example 1:

Find the third quartile (Q₃), given the scores of 9 students in their Mathematics activity, {10, 27, 16, 17, 30, 15, 17, 30, 13}.

• Arrange the data in ascending order: {10,13,15,16,17,17,27,30,30}

• so n = 9

Multiple Choice

The median score is also the __________.

• 1st Quartile

• 2nd Quartile

• 3rd Quartile

• 4th Quartile

Multiple Choice

In the set of scores: 14,17,10,22,19,24,8,12,and 19, the second quartile is ____.

• 13

• 15

• 16

• 17

Multiple Choice

How many percent are below the ninth decile?

• 10%

• 25%

• 90%

• 99%

Multiple Choice

It is a measure that divides the data into one hundred equal parts.

• Percentiles

• Quartiles

• Deciles

• Median