Will the median class and modal class of grouped data always be different? Justify your answer.

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Solution

Understanding the Median class and Modal class of grouped data.
The median class and modal class of grouped data depends on the data given. The value may be the same or different.
Modal class refers to the group of statistical data that is made up of the highest frequencies. It is the class in the frequency distribution table, the consists of the highest number of data points.
The median is the average of the two middle terms. The median class interval is the corresponding class where the median value falls.
Thus, Median class and Modal class of grouped data are not always different.

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Will the median class and modal class of grouped data always be different ? Justify your answer.

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Q. Question 03.
Is it true to say that the mean, mode and median of grouped data will always be different ? Justify your answer.

In the formula for mode of a grouped data,

mode $= l + [\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}] \times h$ ,

where symbols have their usual meaning, $f_{1}$ represents ___.

Q. Question 02.
In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula,

¯ x = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}}

where, a is the assumed mean, a must be one of the mid - point of classes. Is the last statement correct ? Justify your answer.

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