From the following data calculate the quartile deviation: | Marks | 0-15 | 15-30 | 30-45 | 45-60 | 60-75 | 75-90 | 90-105 | | --- | --- | --- | --- | --- | --- | --- | --- | | No. of Students | 8 | 26 | 30 | 45 | 20 | 17 | 4 |

From the following data calculate the quartile dev – Class 12 Business Mathematics And Statistics

Question 26 of 61

From the following data calculate the quartile deviation:

Marks	0-15	15-30	30-45	45-60	60-75	75-90	90-105
No. of Students	8	26	30	45	20	17	4

ChseodishaCHSE Odisha Plus Two (Class 12) Commerce Board 2019Subjective· 8mImportance★★★★★est

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$Q_1 = 31.75$ , $Q_3 = 62.625$ , so quartile deviation $= \dfrac{Q_3-Q_1}{2} \approx 15.44$ marks.

Cumulative frequency table ( $N = \sum f = 150$ ):

Marks	$f$	Cumulative $f$
0–15	8	8
15–30	26	34
30–45	30	64
45–60	45	109
60–75	20	129
75–90	17	146
90–105	4	150

Step 1 — First quartile $Q_1$ . $\dfrac{N}{4} = \dfrac{150}{4} = 37.5$ . The c.f. first exceeding $37.5$ is $64$ , so $Q_1$ lies in class 30–45 ( $L = 30$ , c.f. before $= 34$ , $f = 30$ , $h = 15$ ):

$Q_1 = L + \frac{\tfrac{N}{4} - c.f.}{f}\times h = 30 + \frac{37.5 - 34}{30}\times 15 = 30 + \frac{3.5}{30}\times 15 = 30 + 1.75 = 31.75.$

Step 2 — Third quartile $Q_3$ . $\dfrac{3N}{4} = \dfrac{3\times150}{4} = 112.5$ . The c.f. first exceeding $112.5$ is $129$ , so $Q_3$ lies in class 60–75 ( $L = 60$ , c.f. before $= 109$ , $f = 20$ , $h = 15$ ): …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL1 markMCQ
$Q. From the following the one which is not a measure of dispersion, is :$
(a) Quartile
(b) Mean deviation
(c) Standard deviation
(d) Range
›Reveal solutionSolution

A quartile is a partition value, not a measure of dispersion.

…

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CBSE 2024Set ANNUAL1 mark
$Q. Fill in the blanks : The formula for determining semi-interquartile range is ________.$
›Reveal solutionSolution

Semi-interquartile range $=\dfrac{Q_3-Q_1}{2}$ .

The interquartile range is $Q_3-Q_1$ ; its half is the semi-interquartile range, also called the quartile deviation: …

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CBSE 2022Set ANNUAL1 markMCQ
$Q. The difference between the largest and the smallest quartiles is equal to :$
(a) Quartile deviation
(b) $2 \times$ Quartile deviation
(c) Second quartile
(d) None of the above
›Reveal solutionSolution

$Q_3-Q_1 = 2\times\dfrac{Q_3-Q_1}{2}=2\times$ Quartile deviation.

Quartile deviation (semi-interquartile range) is defined as

$Q.D.=\frac{Q_3-Q_1}{2}.$

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. If the first and the third quartiles are ₹31.75 and ₹62.63 respectively, then their coefficient of quartile deviation is :$
(a) $0.11$
(b) $0.33$
(c) ₹ $0.33$
(d) ₹ $0.11$
›Reveal solutionSolution

$\dfrac{62.63-31.75}{62.63+31.75}=\dfrac{30.88}{94.38}\approx0.33$ .

The coefficient of quartile deviation is

$\frac{Q_3-Q_1}{Q_3+Q_1}.$

With $Q_1=\text{₹}31.75$ and $Q_3=\text{₹}62.63$ :

$Q_3-Q_1=30.88,\qquad Q_3+Q_1=94.38,$ …

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CBSE 2022Set ANNUAL1 markMCQ
$Q_1$
(a) $Q_3 - Q_1$
(b) $\frac{Q_3 - Q_1}{2}$
(c) $\frac{Q_3 - Q_1}{Q_3 + Q_1}$
(d) $\frac{Q_3 + Q_1}{2}$
›Reveal solutionSolution

IQR $=Q_3-Q_1$ (half of it is the quartile deviation).

The interquartile range measures the range covered by the central half of the distribution:

$\text{IQR}=Q_3-Q_1.$

…

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CBSE 2019Set ANNUAL1 mark
$Q. Rectify the underlined portions of the following sentences:$
(ii) <u>Standard</u> deviation is half of the difference between the third and first quartiles.
›Reveal solutionSolution

The correct term is Quartile deviation — $Q.D. = \dfrac{Q_3 - Q_1}{2}$ .

The measure described, one-half of the gap between the upper and lower quartiles, is the quartile deviation, also called the semi-interquartile range:

$Q.D. = \frac{Q_3 - Q_1}{2}$

…

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CBSE 2019Set ANNUAL1 mark
$Q. Fill in the blanks:$
(vii) Semi-interquartile range is also known as __________ deviation.
›Reveal solutionSolution

The blank is Quartile.

The interquartile range is $Q_3 - Q_1$ . Half of it, $\dfrac{Q_3 - Q_1}{2}$ , is called the semi-interquartile range, and this is precisely the definition of the quartile deviation. Hence the tw …

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