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Daftar Isi

- 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

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

- Value 4 is data 1 to 2
- Value 5 is data 3 to 6
- Value 6 is data 7 to 13
- Value 8 is data 14 to 19
- 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**

**4th answer**

**Next Way**To 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.