# Median (Statistics)

See how to find the median of the given values.

4 examples and their solutions.

## Median (Statistics)

### Definition

### Example

Find the median of the given values.

60, 70, 80, 90, 100

Solution
60, 70, 80, 90, 100

60, 70, 80, 90, 100

80

80

Cancel the least value (60)

and the greatest value (100).

Cancel the next least value (70)

and the next greatest value (90).

...

Then the remaining value (80) is the median.

and the greatest value (100).

Cancel the next least value (70)

and the next greatest value (90).

...

Then the remaining value (80) is the median.

Close

### Example

Find the median of the given values.

50, 60, 70, 80, 90, 100

Solution
50, 60, 70, 80, 90, 100

50, 60, 70, 80, 90, 100

(median) = 70 + 802 - [1]

= 1502

= 75

(median) = 70 + 802 - [1]

= 1502

= 75

[1]

After cancelling the least value and the greatest value,

70 and 80 remain.

Then the median is the mean of these two values.

70 and 80 remain.

Then the median is the mean of these two values.

Close

### Formula

n | Median |
---|---|

Odd | n + 12th value |

Even | Mean of n2th value, n2 + 1th value |

use this formula.

### Example

Find the median of the given values.

Solution
Score | Frequency |
---|---|

0 | 1 |

1 | 2 |

2 | 4 |

3 | 7 |

4 | 5 |

5 | 2 |

n = 1 + 2 + 4 + 7 + 5 + 2

= 3 + 11 + 7

= 14 + 7

= 21

21 + 12 = 222

= 11

→ Median: 11th value - [1]

[2]

11th: 3 points - [3]

3 - [4]

= 3 + 11 + 7

= 14 + 7

= 21

21 + 12 = 222

= 11

→ Median: 11th value - [1]

Score | Frequency | Cumulative Frequency |
---|---|---|

0 | 1 | 1 |

1 | 2 | 3 |

2 | 4 | 7 |

3 | 7 | 14 |

4 | 5 | |

5 | 2 |

11th: 3 points - [3]

3 - [4]

[1]

n = 21: odd

→ Median: ([21 + 1]/2)th value

→ Median: ([21 + 1]/2)th value

[2]

Make a Cumulative Frequency column.

Add up the Frequency

and see where the 11th value is in.

1 = 1

1 + 2 = 3

3 + 4 = 7

7 + 7 = 14

Add up the Frequency

and see where the 11th value is in.

1 = 1

1 + 2 = 3

3 + 4 = 7

7 + 7 = 14

[3]

3 points: 8th (7 + 1) ~ 14th

→ 11th: 3 points

→ 11th: 3 points

[4]

Median: 3 (11th)

Close

### Example

Find the median of the given values.

Solution
Score | Frequency |
---|---|

0 | 1 |

1 | 6 |

2 | 8 |

3 | 9 |

4 | 4 |

5 | 2 |

n = 1 + 6 + 8 + 9 + 4 + 2

= 7 + 17 + 6

= 24 + 6

= 30

302 = 15 - [1]

→ Median: Mean of 15th value, 16th value

[2]

15th: 2 points

16th: 3 points - [3]

(median) = 2 + 32 - [4]

= 52

= 7 + 17 + 6

= 24 + 6

= 30

302 = 15 - [1]

→ Median: Mean of 15th value, 16th value

Score | Frequency | Cumulative Frequency |
---|---|---|

0 | 1 | 1 |

1 | 6 | 7 |

2 | 8 | 15 |

3 | 9 | 24 |

4 | 4 | |

5 | 2 |

15th: 2 points

16th: 3 points - [3]

(median) = 2 + 32 - [4]

= 52

[1]

n = 30: even

→ Median: Mean of (30/2)th value, (30/2 + 1)th value

→ Median: Mean of (30/2)th value, (30/2 + 1)th value

[2]

Make a Cumulative Frequency column.

Add up the Frequency

and see where the 15th value and 16 are in.

1 = 1

1 + 6 = 7

7 + 8 = 15

15 + 9 = 24

Add up the Frequency

and see where the 15th value and 16 are in.

1 = 1

1 + 6 = 7

7 + 8 = 15

15 + 9 = 24

[3]

2 points: 8th (7 + 1) ~ 15th

3 points: 16th (15 + 1) ~ 24th

→ 15th: 2 points

16th: 3 points

3 points: 16th (15 + 1) ~ 24th

→ 15th: 2 points

16th: 3 points

[4]

Median: Mean of 2 (15th) and 3 (16th)

Close