Question

Find out the modal-class for the following table:

X	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
Frequency	2	6	4	3	5

A. $1-3$
B. $3-5$
C. $5-7$
D. $7-9$

Answer 1

Hint: The mode of a distribution is the value of an observation which occurs the maximum number of times (highest frequency).
A class is the group / range / interval of data for which the frequencies are given in a grouped data.
The modal class is, therefore, the class-interval (group) with the highest frequency.

Complete step-by-step answer:
The 'modal-class' of a distribution is the class/group which has the highest frequency.
For the given table, class-interval $1-3$ has a frequency of 2, class-interval $3-5$ has a frequency of 6, and so on.
The highest frequency is 6 and it is for class-interval $3-5$ . Therefore $3-5$ is the modal-class (mode) of the given distribution.

Note: Mode is one of the most common ways to describe a set of data. The Mean (average) and Median of a distribution (set of data) usually revolves around the Mode.
Empirical Relationship between Mean, Median and Mode: In case of a moderately skewed distribution, the difference between mean and mode is almost equal to three times the difference between the mean and median:
 $Mean-Mode=3\left( Mean-Median \right)$
For a normal distribution (symmetrical frequency curve, most values fall towards the center), then mean, median, and mode will be equal: $Mean=Median=Mode$ .
For a positively skewed distribution (skewed towards left, a majority of the observations are small), the mean is always greater than median and the median is always greater than the mode: $Mean>Median>Mode$ .
For a negatively skewed distribution (skewed towards right, a majority of the observations are big), the mean is always lesser than median and the median is always lesser than the mode: $Mean