# Quartile

See how to find the quartiles of the given values (Q_{1}, Q_{2}, Q_{3}).

2 examples and their solutions.

## Quartiles

### Definition

Q

The quartiles (Q_{1}Q_{2}Q_{3}_{1}, Q

_{2}, Q

_{3}) are the values

that divide the values into 4 parts.

Q

_{1}: Median of the left half (less side)

Q

_{2}: Median of the whole values

Q

_{3}: Median of the right half (greater side)

### Example

Find the quartiles of the given values.

1, 2, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9

Solution 1, 2, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9

1, 2, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9 - [1]

Q

Q

_{2}= 6[1]

Q

_{2}: Median of the whole values↓

1, 2, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9 - [2]

Q

Q

_{1}= 4[2]

Q

_{1}: Median of the left half↓

1, 2, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9 - [3]

Q

Q

_{3}= 7[3]

Q

_{3}: Median of the right half↓

1, 2, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9

Q

Q

Q

Q

_{1}= 4Q

_{2}= 6Q

_{3}= 7Close

### Example

Find the quartiles of the given values.

1, 2, 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

Solution 1, 2, 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

1, 2, 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9 - [1]

↑

Q

= 6.5

↑

Q

_{2}= 6 + 72= 6.5

[1]

↓

1, 2, 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9 - [2]

↑

6.5

Q

↑

6.5

Q

_{1}= 4[2]

Q

→ Q

_{2}= 6.5→ Q

_{1}: Median of 1 ~ 6↓

1, 2, 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9 - [3]

↑

6.5

Q

↑

6.5

Q

_{3}= 7[3]

Q

→ Q

_{2}= 6.5→ Q

_{3}: Median of 7 ~ 9↓

1, 2, 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

↑

6.5

Q

Q

Q

↑

6.5

Q

_{1}= 4Q

_{2}= 6.5Q

_{3}= 7Close