# Does a data set always have a mode?

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16
Sep 22, 2015

Data set need not always have a mode.

#### Explanation:

Mode is an item that occurs more number of times in a distribution.
Here the distribution, I mean Individual Observation.

In an Individual Observation, if each item occurs only once, you will not get mode.

In a Discrete Distribution and Continuous Distribution, there is mode always.

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6
Dec 7, 2015

Nope.

#### Explanation:

Not all data sets have a mode. For example, consider the following hypothetical set of mean temperature measurements for 10 consecutive days in degress C:

Day Temp
$1 \rightarrow 23.0$
$2 \rightarrow 22.9$
$3 \rightarrow 22.5$
$4 \rightarrow 23.4$
$5 \rightarrow 22.4$
$6 \rightarrow 22.8$
$7 \rightarrow 23.6$
$8 \rightarrow 23.1$
$9 \rightarrow 21.2$
$10 \rightarrow 22.1$

We can see that the data set has no mode , since each measurement is different from all the others. Therefore the frequency for each observation is 1. Therefore this data set has no mode.

Consider another set of measurements for another set of 10 consecutive days

Day Temp
$1 \rightarrow 23.0$
$2 \rightarrow 22.9$
$3 \rightarrow 22.5$
$4 \rightarrow 23.4$
$5 \rightarrow 23.0$
$6 \rightarrow 22.8$
$7 \rightarrow 23.0$
$8 \rightarrow 23.1$
$9 \rightarrow 21.2$
$10 \rightarrow 22.1$

One can see that the observation 23.0C has frequency equal to 3 ( Days 1, 5 and 7 ). Hence, the mode for this set is 23.0. Since we have one mode , this set is UNIMODAL.

Consider further another set of measurements for another set of 10 consecutive days

Day Temp
$1 \rightarrow 21.0$
$2 \rightarrow 22.9$
$3 \rightarrow 23.1$
$4 \rightarrow 23.1$
$5 \rightarrow 22.4$
$6 \rightarrow 23.1$
$7 \rightarrow 21.0$
$8 \rightarrow 23.8$
$9 \rightarrow 21.2$
$10 \rightarrow 21.0$

One can see that the observations ${21.0}^{o} C$ has frequency equal to 3 ( Days 1, 7 and 10 ). The observation ${23.1}^{o} C$ has frequency also equal to 3 ( Days 3,4 and 6 ). Hence, the modes for this set are 21.0 and 23.1. Since we have two modes , this set is MULTIMODAL.

Therefore, a set can have either:
1. No mode
2. One mode - Unimodal
3. More than one mode - Multimodal

Hope this helps.

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5
K S. Share
Sep 18, 2015

No

#### Explanation:

some sets don't have modes because all their number are the same.

So for example in a histogram, the events could take place at the same time so there would be no mode.

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