# Please explain how to find the quartile deviation

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## Please explain how to find the quartile deviation

How to find the quartile deviation. Quartiles are measures that divide data into four equal parts. The quartiles consist of the lower quartile (Q₁), the middle quartile (Q₂/median) and the upper quartile (Q₃). The quartile deviation is half of the difference between the upper and lower quartiles.

• Quartile deviation = ½ (Q₃ – Q₁)

To determine the quartile value, the data must first be sorted from smallest to largest.

If the number of data n is odd

• Q₁ = data to ¼ (n + 1)
• Q₂ = data to ½ (n + 1)
• Q₃ = data to ¾ (n + 1)

If the number of data n is even

• Q₁ = data to ¼ (n + 2)
• Q₂ = ½ (data to ½ n + data to (½ n + 1))
• Q₃ = data to ¼ (3n + 2)

### Discussion Details find the quartile deviation

To determine the quartile deviation, we have to find the 1st and 3rd quartiles first, then all we have to do is plug them into the formula, namely:

• Quartile deviation = ½ (Q₃ – Q₁)

Let's take an example

The quartile deviation of the following data is

Value 4 5 6 8 10

Cumulative frequency 2 4 7 6 1

Java

To find the quartiles of the table, we also make cumulative frequencies

Value | frequency | cumulative frequency

4            2              2

5            4              2 + 4 = 6

6            7              6 + 7 = 13

8            6              13 + 6 = 19

10           1              19 + 1 = 20

From the order of the table, based on the frequency, the meaning is

1. Value 4 is data 1 to 2
2. Value 5 is data 3 to 6
3. Value 6 is data 7 to 13
4. Value 8 is data 14 to 19
5. Value 10 is data to 20

#### Because n = 20 even numbers so:

Q₁ = data to ¼ (n + 2)

Q₁ = data to ¼ (20 + 2)

Q₁ = data to 5.5

Q₁ = ½ (5th data + 6th data)

Q₁ = ½ (5 + 5)

Q₁ = ½ (10)

Q₁ = 5

Q₃ = data to ¼ (3n + 2)

Q₃ = data to ¼ (3(20) + 2)

Q₃ = data to ¼ (60 + 2)

Q₃ = data to ¼ (62)

Q₃ = data to 15.5

Q₃ = ½ (15th data + 16th data)

Q₃ = ½ (8 + 8)

Q₃ = ½ (16)

Q₃ = 8

So the quartile deviation of the data is

= ½ (Q₃ – Q₁)

= ½ (8 – 5)

= ½ (3)

= 1,5

Next WayTo make it easier for us, we can do it manually, that is, the data is sorted from largest to smallest:

4  4  5  5  5  5  6  6  6  6  6  6  6  8  8  8  8  8  8  10

• The median (Q₂) or the midpoint is between the 10th and 11th data, namely 6
• Q₁ is the midpoint of the data to the left of the median, which is 5
• Q₃ is the midpoint of the data to the right of the median, which is 8

4  4  5  5  5 | 5  6  6  6  6 | 6  6  6  8  8 | 8  8  8  8  10

Q₁ Q₂ Q₃

So the quartile deviation of the data is

= ½ (Q₃ – Q₁)

= ½ (8 – 5)

= ½ (3)

= 1,5

### Question Details

Class : 9

Course : Mathematics

Category : Statistics

Keywords : How to find the quartile deviation.

This is the discussion that we have compiled from various sources by the Katalistiwa team. May be useful.