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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	$15$	$110$	$135$	$115$	$25$

Class interval	Frequency
$0-10$	$5$
$10-20$	$x$
$20-30$	$20$
$30-40$	$15$
$40-50$	$y$
$50-60$	$5$
Total	$60$

Life time (in hours)	Number of lamps
$1500-2000$	$14$
$2000-2500$	$56$
$2500-3000$	$60$
$3000-3500$	$86$
$3500-4000$	$74$
$4000-4500$	$62$
$4500-5000$	$48$

Number of students per teacher	Number of states/$U$.$T$.
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

Class interval	$10-25$	$25-40$	$40-55$	$55-70$	$70-85$	$85-100$
Number of students	$2$	$3$	$7$	$6$	$6$	$6$

Similar Questions

If the median of the distribution given below is $28.5,$ find the values of $x$ and $y$.
Class interval Frequency
$0-10$ $5$
$10-20$ $x$
$20-30$ $20$
$30-40$ $15$
$40-50$ $y$
$50-60$ $5$
Total $60$

The following table gives the distribution of the lifetime of $400$ neon lamps:
Life time (in hours) Number of lamps
$1500-2000$ $14$
$2000-2500$ $56$
$2500-3000$ $60$
$3000-3500$ $86$
$3500-4000$ $74$
$4000-4500$ $62$
$4500-5000$ $48$

Find the median lifetime of a lamp.

The marks distribution of $30$ students in a mathematics examination is given in the table. Find the mode of this data. Also,compare and interpret the mode and the mean.
Class interval $10-25$ $25-40$ $40-55$ $55-70$ $70-85$ $85-100$
Number of students $2$ $3$ $7$ $6$ $6$ $6$

The median of the following data is $525$. Find the values of $x$ and $y$,if the total frequency is $100$.
Class interval Frequency
$0-100$ $2$
$100-200$ $5$
$200-300$ $x$
$300-400$ $12$
$400-500$ $17$
$500-600$ $20$
$600-700$ $y$
$700-800$ $9$
$800-900$ $7$
$900-1000$ $4$

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Class interval	Frequency
$0-100$	$2$
$100-200$	$5$
$200-300$	$x$
$300-400$	$12$
$400-500$	$17$
$500-600$	$20$
$600-700$	$y$
$700-800$	$9$
$800-900$	$7$
$900-1000$	$4$

Similar Questions

If the median of the distribution given below is $28.5,$ find the values of $x$ and $y$.Class intervalFrequency$0-10$$5$$10-20$$x$$20-30$$20$$30-40$$15$$40-50$$y$$50-60$$5$Total$60$

The following table gives the distribution of the lifetime of $400$ neon lamps:Life time (in hours)Number of lamps$1500-2000$$14$$2000-2500$$56$$2500-3000$$60$$3000-3500$$86$$3500-4000$$74$$4000-4500$$62$$4500-5000$$48$Find the median lifetime of a lamp.

The marks distribution of $30$ students in a mathematics examination is given in the table. Find the mode of this data. Also,compare and interpret the mode and the mean.Class interval$10-25$$25-40$$40-55$$55-70$$70-85$$85-100$Number of students$2$$3$$7$$6$$6$$6$

The median of the following data is $525$. Find the values of $x$ and $y$,if the total frequency is $100$.Class intervalFrequency$0-100$$2$$100-200$$5$$200-300$$x$$300-400$$12$$400-500$$17$$500-600$$20$$600-700$$y$$700-800$$9$$800-900$$7$$900-1000$$4$