Lower quartile, upper quartile and interquartile range...

Lower quartile, upper quartile and interquartile range respectively are $\mathrm{Q}_{1}, \mathrm{Q}_{3}$ and $\mathrm{Q}$. If the average of $\mathrm{Q}, \mathrm{Q}_{1}$ and $\mathrm{Q}_{3}$ is 40 and semi-interquartile range is 6, then find the lower quartile. (1) 24 (2) 36 (3) 48 (4) 60

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Key Concepts

Averages of Statistical Measures

Averaging specific statistical measures, such as combining the interquartile range and quartiles, can provide insight into the overall distribution of the data. This involves algebraic manipulation and understanding relationships between various summary statistics to derive unknown values.

Semi-Interquartile Range

The semi-interquartile range is half of the interquartile range. This measure provides a sense of the average spread of the data around the median, and it is often used as a statistic to describe the dispersion of a data set while reducing the effect of extreme values.

Interquartile Range (IQR)

The interquartile range is the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the range within which the central 50% of the data lie, offering a robust measure of variability that is less influenced by outliers compared to the total range.

Quartiles

Quartiles divide a data set into four equal parts. The lower quartile (Q1) marks the 25th percentile, the median marks the 50th percentile, and the upper quartile (Q3) marks the 75th percentile. Understanding quartiles is essential for summarizing data distributions and identifying the spread of the middle half of the data.

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