Question

Find the mode of the following series:
\[7.5\], \[7.3\], \[7.2\], \[7.2\], \[7.4\], \[7.7\], \[7.7\], \[7.5\], \[7.3\], \[7.2\], \[7.6\], \[7.2\]

Answer 1

Hint: Here, we need to find the mode of the given series. First, we will write the series in increasing order. Then, we will find the frequency of each observation. Finally, we will find the mode of the series. The mode of an individual series is the observation with the highest frequency.

Complete step-by-step answer:
The given series is an individual series.
First, we will write this series in increasing order.
\[7.2\], \[7.2\], \[7.2\], \[7.2\], \[7.3\], \[7.3\], \[7.4\], \[7.5\], \[7.5\], \[7.6\], \[7.7\], \[7.7\]
The frequency of an observation is the number of times it appears in the series.
The observation \[7.2\] comes 4 times in the series.
Therefore, the frequency of the observation \[7.2\] is 4.
Similarly, we can find the frequencies of the other observations.
The observation \[7.3\] comes 2 times in the series.
Therefore, the frequency of the observation \[7.3\] is 2.
The observation \[7.4\] comes 1 time in the series.
Therefore, the frequency of the observation \[7.4\] is 1.
The observation \[7.5\] comes 2 times in the series.
Therefore, the frequency of the observation \[7.5\] is 2.
The observation \[7.6\] comes 1 time in the series.
Therefore, the frequency of the observation \[7.6\] is 1.
The observation \[7.7\] comes 2 times in the series.
Therefore, the frequency of the observation \[7.7\] is 2.
The mode of an individual series is the observation that repeats the most.
It is the observation with the highest frequency.
Now, we can observe that out of the 12 observations, the \[7.2\] has a frequency of 4, that is it comes 4 times in the series.
Therefore, the mode of the given series is \[7.2\].

Note: The given series is an individual series. An individual series is a series in which the items are shown individually. We can also find the mode of the series by constructing a frequency distribution table, and using tally marks, find the frequency of each observation in tabular form.