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(D) The class intervals are not continuous. The gap between two consecutive class intervals is $1$. To make them continuous,we subtract $0.5$ from the

Vedclass · Accepted Answer

$57.19$

Vedclass · Answer

(D) The class intervals are not continuous. The gap between two consecutive class intervals is $1$. To make them continuous,we subtract $0.5$ from the lower limit and add $0.5$ to the upper limit of each class.Class interval$f_i$$x_i$$d_i = x_i - 57$$u_i = d_i / 3$$f_i u_i$$49.5-52.5$$15$$51$$-6$$-2$$-30$$52.5-55.5$$110$$54$$-3$$-1$$-110$$55.5-58.5$$135$$57$$0$$0$$0$$58.5-61.5$$115$$60$$3$$1$$115$$61.5-64.5$$25$$63$$6$$2$$50$Total$400$$25$Here,$\sum f_i = 400$,$\sum f_i u_i = 25$,assumed mean $a = 57$,and class size $h = 3$.Using the step-deviation method:$\bar{x} = a + \left( \frac{\sum f_i u_i}{\sum f_i} ight) 	imes h$$\bar{x} = 57 + \left( \frac{25}{400} ight) 	imes 3 = 57 + \frac{75}{400} = 57 + 0.1875 = 57.1875 \approx 57.19$.We chose the step-deviation method because the values of $f_i$ and $d_i$ are large and there is a common factor $h=3$.

Number of mangoes	$50$-$52$	$53$-$55$	$56$-$58$	$59$-$61$	$62$-$64$
Number of boxes	$15$	$110$	$135$	$115$	$25$

Literacy rate (in $\%$)	$45-55$	$55-65$	$65-75$	$75-85$	$85-95$
Number of cities	$3$	$10$	$11$	$8$	$3$

Monthly consumption (in units)	Number of consumers
$65-85$	$4$
$85-105$	$5$
$105-125$	$13$
$125-145$	$20$
$145-165$	$14$
$165-185$	$8$
$185-205$	$4$

Profit (Rs in lakhs)	Number of shops (frequency)
More than or equal to $5$	$30$
More than or equal to $10$	$28$
More than or equal to $15$	$16$
More than or equal to $20$	$14$
More than or equal to $25$	$10$
More than or equal to $30$	$7$
More than or equal to $35$	$3$

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Similar Questions

The following table gives the literacy rate (in percentage) of $35$ cities. Find the mean literacy rate.
Literacy rate (in $\%$) $45-55$ $55-65$ $65-75$ $75-85$ $85-95$
Number of cities $3$ $10$ $11$ $8$ $3$

The following table gives the production yield per hectare of wheat of $100$ farms of a village.
Production yield (in kg/ha) Number of farms
$50-55$ $2$
$55-60$ $8$
$60-65$ $12$
$65-70$ $24$
$70-75$ $38$
$75-80$ $16$

Change the distribution to a 'more than type' distribution,and draw its ogive.

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Production yield (in kg/ha)	Number of farms
$50-55$	$2$
$55-60$	$8$
$60-65$	$12$
$65-70$	$24$
$70-75$	$38$
$75-80$	$16$