# Mode of Ungrouped Data

The mode or modal value is that value in a series of observations which occur with the greatest frequency e.g. the mode of the series 3, 5, 8, 5, 4, 5, 9, 3 would be 5.Â Since this value occurs most frequently than any of the other values.

The mode of a distribution is the value at the point around which the items bind to be most heavily concentrated. It is regarded as the most typical or fashionable value of distribution.

The following diagram shows the modal value:Â Â Â

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The value of the variable of which the curve reaches the maximum is called the mode. The value around which the items tend to be most heavily concentrated.

There are many situations in which arithmetic mean and median fail to reveal the true characteristics of data.

For example, where we talk of the most common wage.

Most Common Income, most common height, most common size of the shoe or readymade garment we have to find out mode, because in these cases arithmetic mean and median cannot represent the data.

For example if the data are:

Â

Size ofÂ Â shoesÂ Â Â Â |
5 |
6 |
7 |
8 |
9 |
10 |
11 |

No. ofÂ Â Â personsÂ Â |
10 |
20 |
25 |
40 |
22 |
15 |
6 |

Now in this case if we have to find out the average shoe size, arithmetic mean cannot represent it. This series can be represented only by mode.

The modal size in 8, since more persons are wearing this size compared to others.