# **Mean, Median, and Mode**

- Sometimes you get very similar results with all three.
- Like when you have a normal distribution.

# **Mean**

#### Usually, the mean is preferred:

- It uses all the scores ( so it’s representative of the entire data set ).
- It’s used to compute the variance and SD.
- It’s good for inferential statistics.
- Note that you should have interval or ratio data to compute a mean.

# **Median**

- Use the median when you have extreme you have extreme scores or a skewed distribution

# **Median**

- Use the median when you have extreme scores or skewed distribution.
- Example :
- X = 10, 11, 11, 11, 11, 12, 12, 13, 13, 100
- M = 20.3
- Median = 11.5
- Median represents most of the distribution best .

# **Median**

- In psychology, you might encounter an open-ended distribution like this:
- N = 20
- Cannot compute a mean.
- Median = 1.5
- Use the median!

Number of Children | Frequency |

5 or more | 32 |

4 | 2 |

3 | 2 |

2 | 3 |

1 | 6 |

0 | 4 |

**Median**

- Use the median if you have ordinal data
- Remember, the mean balances distance
- With ordinal data, you don’t have equal distances between data points

**Mode**

- Use the mode if you have nominal data
- Example:

Hair color: 1= brown , 2 = black , 3 = blond 4 = red

Hair color | Frequency |

4 | 2 |

3 | 4 |

2 | 5 |

1 | 7 |

N=18

# **Mode**

- If you have a discrete variable like a number of children, you can compute a mean.
- In this case, means are fractional values that can’t really exist. EXAMPLE: “The average family has 2.5 kids”
- The mode identifies the typical case: – “The typical family has 2 kids.” – “The modal age for spinal cord injury is 19.”

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