Consider the following frequency distribution of the heights...

Consider the following frequency distribution of the heights of 60 students of a class: $$ \begin{array}{|l|l|} \hline \text { Height (in cm) } & \text { No. of students } \\ \hline 150-155 & 15 \\ \hline 155-160 & 13 \\ \hline 160-165 & 10 \\ \hline 165-170 & 8 \\ \hline 170-175 & 9 \\ \hline 175-180 & 5 \\ \hline \end{array} $$ The sum of the lower limit of the modal class and upper limit of the median class is: (a) 310 (b) 315 (c) 320 (d) 330

Consider the following frequency distribution of the heights of 60 students of a class:
$$
\begin{array}{|l|l|}
\hline \text { Height (in cm) } & \text { No. of students } \\
\hline 150-155 & 15 \\
\hline 155-160 & 13 \\
\hline 160-165 & 10 \\
\hline 165-170 & 8 \\
\hline 170-175 & 9 \\
\hline 175-180 & 5 \\
\hline
\end{array}
$$
The sum of the lower limit of the modal class and upper limit of the median class is:
(a) 310
(b) 315
(c) 320
(d) 330

Key Concepts

Frequency Distribution

A frequency distribution is a summary that shows the number of observations within specified intervals or classes. It is used to organize raw data into a structured format to help identify patterns, trends, and central tendencies within the dataset.

Grouped Data

Grouped data is data that has been organized into intervals or classes rather than being listed individually. This organization helps in simplifying and analyzing large datasets, particularly when dealing with continuous variables.

Modal Class

The modal class is the group or interval in a frequency distribution that has the highest frequency of observations. It is used as a representative of the most common range of values and assists in identifying the mode when dealing with grouped data.

Median Class

The median class is the interval that contains the median, which is the middle value in an ordered dataset. It is identified through the cumulative frequency distribution by locating the class interval where the cumulative count reaches or exceeds half of the total number of observations.

Cumulative Frequency

Cumulative frequency is the running total of frequencies through the classes in a frequency distribution. This concept is especially useful for determining the median class, as it allows for the calculation of the point where the dataset is divided into two equal halves.

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