# What Does Mode Mean in Math?

Mode is defined as the most frequently occurring observation in the data .it is the observation that occurs the maximum number of times in the given data.

**What is Mode?**

Mode is defined as the most frequently occurring observation in the data .it is the observation that occurs the maximum number of times in the given data.

The following formula is used to determine the mode.

**Ungroup data and discrete data**

Mode =the most frequent observation

**Group data (continuous)**

The following steps are involved in determining the mode for group data.

- Find the group that has the maximum frequency
- Use the formula

Mode=l+(f_{m}-f_{1}/2f_{m}-f_{1}-f_{2})Xh

Where,

l=lower class boundary of the modal class or group

h=class interval size of the modal class

f_{m}=frequency of the modal class

f_{1}=frequency of the class preceding the modal class

f_{2}=frequency of the class succeeding the modal class

**For example:**

Find the modal for the following data.

4,4,5,5,6,6,6,7,7,5,7,5,8,8,8,6,5,6,5,7

Solution: we note the most occurring observation in the given data and find that mode.

Mode=6

For example: Find Mode for the following frequency distribution.

(No of heads)X | Frequency |

1 | 3 |

2 | 8 |

3 | 5 |

4 | 3 |

5 | 1 |

Solution: Since the given data is discrete grouped data so that,

Mode =2

Since for X=2 the frequency is maximum, means 2 heads appear the maximum number of times i.e 8

**For example**:

For the following data showing weights of toffee boxes in gm. determine the modal weight of boxes.

Classes /Group | Frequency |

0–9 | 2 |

10–19 | 10 |

20–29 | 5 |

30–39 | 9 |

40–49 | 6 |

50–59 | 7 |

60–69 | 1 |

Solution: Since the data continues so we proceed as follows.

- First, determine the class boundaries
- Find the class with a maximum frequency

Classes /Groups | Class boundaries | Frequency |

0–9 | -0.5â€”9.5 | 2 |

10–19 | 9.5â€”19.5 | 10 |

20–29 | 19.5â€”29.5 | 5 |

30–39 | 29.5â€”39.5 | 9 |

40–49 | 39.5â€”49.5 | 6 |

50–59 | 49.5â€”59.5 | 7 |

60–69 | 59.5â€”69.5 | 1 |

total | Sigmaf=40 |

From the above table, we get,

Modal class of group= 9.5â€”19.5.

f_{m}=10

l=9.5

h=10

f_{1}=2

f_{2}=5

By using formula

Mode=l+(f_{m}-f_{1}/2f_{m}-f_{1}-f_{2})Xh

Mode=9.5+(10-2/2(10)-2-5)x10

Mode =9.5+80/20-7

Mode =9.5+80/13

Mode=9.5+6.134

Mode=15.654

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