Calculate the quartile deviation for the following distribution : | Class interval | Frequency | | --- | --- | | 0 – 15 | 7 | | 15 – 30 | 26 | | 30 – 45 | 30 | | 45 – 60 | 45 | | 60 – 75 | 20 | | 75 – 90 | 17 | | 90 – 105 | 5 |

Calculate the quartile deviation for the following – Class 12 Business Mathematics And Statistics

Question 60 of 61

Calculate the quartile deviation for the following distribution :

Class interval	Frequency
0 – 15	7
15 – 30	26
30 – 45	30
45 – 60	45
60 – 75	20
75 – 90	17
90 – 105	5

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Find $Q_1=32.25$ , $Q_3=63.375$ ; $Q.D.=\dfrac{Q_3-Q_1}{2}=15.5625$ .

Step 1 — cumulative frequencies ( $N=150$ ):

Class	$f$	cf
0 – 15	7	7
15 – 30	26	33
30 – 45	30	63
45 – 60	45	108
60 – 75	20	128
75 – 90	17	145
90 – 105	5	150

Step 2 — $Q_1$ : $\dfrac{N}{4}=\dfrac{150}{4}=37.5$ . First cf $\ge37.5$ is $63$ , so $Q_1$ class $=30\text{–}45$ ( $L=30,\ cf=33,\ f=30,\ h=15$ ):

$Q_1=L+\frac{\frac{N}{4}-cf}{f}\times h=30+\frac{37.5-33}{30}\times15=30+\frac{4.5}{30}\times15=30+2.25=32.25.$

Step 3 — $Q_3$ : $\dfrac{3N}{4}=\dfrac{450}{4}=112.5$ . First cf $\ge112.5$ is $128$ , so $Q_3$ class $=60\text{–}75$ ( $L=60,\ cf=108,\ f=20,\ h=15$ ): …

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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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←Previous questionQ44 — Write the other name of semi-interquartile range and state the formula…→Next questionQ46 — Explain the characteristics of an ideal measure of dispersion.

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