Calculate the values of (i) mean, (ii) median, and (iii) the...

Calculate the values of (i) mean, (ii) median, and (iii) the two quartiles: Income \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} \hline$(R s$ 'ooo): Under & 1 & $1-2$ & $2-3$ & $3-5$ & $5-10$ & $10-25$ & $25-50$ & $50-100$ & $100-1000$ \\ \hline No. of Persons: & 13 & 90 & 81 & 117 & 66 & 27 & 6 & 2 & 2 \\ \hline \end{tabular}

Calculate the values of (i) mean, (ii) median, and (iii) the two quartiles:
Income \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline$(R s$ 'ooo): Under & 1 & $1-2$ & $2-3$ & $3-5$ & $5-10$ & $10-25$ & $25-50$ & $50-100$ & $100-1000$ \\
\hline No. of Persons: & 13 & 90 & 81 & 117 & 66 & 27 & 6 & 2 & 2 \\
\hline
\end{tabular}

Key Concepts

Quartiles Calculation in Grouped Data

Quartiles divide the dataset into four equal parts. To estimate the first and third quartiles in grouped data, the cumulative frequency is used to find the classes corresponding to one-quarter and three-quarters of the total frequency, respectively. Linear interpolation within these classes then provides approximate values for the quartiles, giving insights into the data's spread.

Median Calculation in Grouped Data

The median for grouped data is estimated by finding the class interval where the cumulative frequency reaches or exceeds half of the total frequency. Within this median class, linear interpolation is used to approximate the exact median value. This process accounts for the uneven distribution of data across the intervals.

Grouped Frequency Distribution

A grouped frequency distribution organizes raw data into intervals (or groups) with corresponding frequencies, making it easier to analyze large datasets. It simplifies the data representation and allows for efficient computation of descriptive statistics by summarizing individual values into manageable groups.

Arithmetic Mean for Grouped Data

The arithmetic mean in grouped data is calculated by taking the midpoint of each class interval, multiplying it by the frequency of that class, summing these products, and then dividing by the total frequency. This weighted average approximates the central tendency of the data when exact individual values are not available.

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