An incomplete frequency distribution is given below: Height (inches) 5.1-6.0 6.1-7.0

step 1 Okay, in this question we are given a data where we are given height of certain students and we

An incomplete frequency distribution is given below: Height...

An incomplete frequency distribution is given below: \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline Height (inches) & $5.1-6.0$ & $6.1-7.0$ & $7.1-8.0$ & $8.1-9.0$ & $9.1-10.0$ & $10.1-11.0$ & $11.1-12.0$ \\ \hline No. of Plants & 3 & 8 & 27 & $?$ & 17 & 11 & 9 \\ \hline \end{tabular} It is known that the median height of the plant is $8.53$ inches. Calculate the $\begin{array}{ll}\text { missing frequency. } & \text { [I.C.W.A., Jan. '72] }\end{array}$

An incomplete frequency distribution is given below:
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline Height (inches) & $5.1-6.0$ & $6.1-7.0$ & $7.1-8.0$ & $8.1-9.0$ & $9.1-10.0$ & $10.1-11.0$ & $11.1-12.0$ \\
\hline No. of Plants & 3 & 8 & 27 & $?$ & 17 & 11 & 9 \\
\hline
\end{tabular} It is known that the median height of the plant is $8.53$ inches. Calculate the $\begin{array}{ll}\text { missing frequency. } & \text { [I.C.W.A., Jan. '72] }\end{array}$

Key Concepts

Grouped Data

Grouped data refers to data that has been organized into classes or intervals rather than individual values. This method is useful for large data sets or continuous data, where precise values are less important than the range in which they fall, allowing for more efficient analysis and visualization.

Median of Grouped Data

The median of grouped data is a measure of central tendency that identifies the middle value in a frequency distribution. Since individual data points aren't available, the median is estimated using the median class, cumulative frequencies, and interpolation techniques to pinpoint an approximate location where half the data values lie below and half above.

Cumulative Frequency

Cumulative frequency is the progressive total of frequencies through the classes in a frequency distribution. It is used to determine the number of observations that fall below the upper boundary of each class, which is essential for identifying the median class and other percentile-related analyses.

Interpolation

Interpolation in the context of grouped data is a method used to estimate the value of a variable within an interval when only class limits and frequencies are known. It involves assuming a uniform distribution of data within the class to more accurately predict the median value or other statistical measures.

Frequency Distribution

A frequency distribution is a way to organize data so that you can see how often each value, or range of values, occurs. It summarizes raw data into groups or classes with corresponding frequencies, making it easier to identify patterns, trends, and distributions in the data.

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