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The formula to calculate the coefficient of quartile deviation is

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HTET TGT Mathematics 2020 Official Paper
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  1. \(\frac{Q_3 - Q_1}{Q_3 + Q _1}\)
  2. \(\frac{Q_3 + Q_1}{4}\)
  3. \(\frac{Q_1 - Q_2}{4}\)
  4. \(\frac{Q_2 + Q_1}{Q_2 - Q _1}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{Q_3 - Q_1}{Q_3 + Q _1}\)
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Explanation:

Quartile deviation is a statistic that measures the deviation. It measures the deviation of the data from the average value.

Here we have three quartiles Q1, Q2, Q3 which divide the data into three quarters. The median of the data has been referred as the second quartile Q2. Also, the first quartile Q1 is the median of the first half of the data, and the third quartile Q3 is the median of the second half of the data.

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Quartile Deviation =(Q3 – Q1) / 2

Quartile deviation can be calculated for both the grouped data and the ungrouped data. Quartile deviation measures the absolute level of dispersion and is not affected by the extreme values. And the relative measure with reference to quartile deviation is known as the coefficient of quartile deviation.

Coefficient of quartile deviation = \(\frac{Q_3 - Q_1}{Q_3 + Q _1}\)

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