# Concept of Mode

Mode is the value which occurs the greatest number of times in the data. When each value occurs the same number of times in the data, there is no mode. If two or more values occur the same number of times, then there are two or more modes and the distribution is said to be multi-mode. If the data has only one mode the distribution is said to be uni-model, and for data having two modes the distribution is said to be bi-model.

__Mode from Ungrouped Data__

Mode is calculated from ungrouped data by inspecting the given data. We pick out the value which occurs the greatest number of times in the data.

__Mode from Grouped Data__

With frequency distribution with equal class interval sizes, the class which has the maximum frequency is called the model class.

\[Mode = l + \frac{{{f_m} – {f_1}}}{{\left( {{f_m} – {f_1}} \right) + \left( {{f_m} – {f_2}} \right)}} \times h\]

Here

$$l$$= Lower class boundary of the model class

$${f_m}$$= Frequency of the model class (maximum frequency)

$${f_1}$$= Frequency preceding the model class frequency

$${f_2}$$= Frequency following the model class frequency

$$h$$= Class interval size of the model class

__Mode from Discrete Data__

When the data follows a discrete set of values, the mode may be found by inspection. The mode is the value of *X* corresponding to the maximum frequency.

__Example__:

Find the mode of the values **5, 7, 2, 9, 7, 10, 8, 5, 7**

__Solution__:

The mode is **7** because it occurs the greatest number of times in the data.

__Example__:

The weights of 50 college students are given in the following table. Find the mode of the distribution.

Weight (Kg) |
60 – 64 |
65 – 69 |
70 – 74 |
75 – 79 |
80 – 84 |

No of Students |
5 |
9 |
16 |
12 |
8 |

__Solution__**:**

Weight (Kg) |
No of Studentsf |
Class Boundary |

60 – 64 |
5 |
59.5 – 64.5 |

65 – 69 |
9 |
64.5 – 69.5 |

70 – 74 |
16 |
69.5 – 74.5 |

75 – 79 |
12 |
74.5 – 79.5 |

80 – 84 |
8 |
79.5 – 84.5 |

\[Mode = l + \frac{{{f_m} – {f_1}}}{{\left( {{f_m} – {f_1}} \right) + \left( {{f_m} – {f_2}} \right)}} \times h\]

\[Mode = 69.5 + \frac{{19 – 9}}{{\left( {16 – 9} \right) + \left( {16 – 12} \right)}} \times 5\]

\[Mode = 69.5 + \frac{7}{{7 + 4}} \times 5 = 72.68\]

Hasan

August 26@ 5:44 pmif the ungroup data is 1,2,3,4,5,6,7,8

then what is the mode of this data!!!!!! all are edual number of numbers..

Jay

March 17@ 12:09 pmThere is no mode on that set of data.

Grace Njuguna

February 24@ 11:06 pmA certain question was given to us during a test at school. Can someone help me out???

The question was as below..

40 students took up a test. The results of those who passed are given below.

Marks. 4 5 6 7 8 9

Freq. 8 10 9 6 4 3

Find the:

(a) Average marks. (3 marks)

(b) Standard deviation (4 marks)

(c) Mode (3 marks)

(d) Median (3 marks)

Jay

March 17@ 12:14 pmIf f sub m is the maximum number of model class, how come in your example they have different values? The numerator is 19 and on the denominator it’s 16?

Japhz

August 26@ 9:00 amWhat if in the grouped data there are two modes? ? Need help!

shehlla

September 29@ 6:51 pmthen there will be two mode, simple!