The mean of the following frequency distribut | vedclass

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(B) To find the missing frequency $f$,we use the step-deviation method for mean: $\bar{x} = A + \left( \frac{\sum f_i u_i}{\sum f_i} ight) 	imes c$

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(B) To find the missing frequency $f$,we use the step-deviation method for mean: $\bar{x} = A + \left( \frac{\sum f_i u_i}{\sum f_i} ight) 	imes c$.ClassFrequency $(f_i)$Midpoint $(x_i)$$u_i = \frac{x_i - A}{c}$$f_i u_i$$0-10$$8$$5$$-4$$-32$$10-20$$4$$15$$-3$$-12$$20-30$$20$$25$$-2$$-40$$30-40$$45$$35$$-1$$-45$$40-50$$64$$45=A$$0$$0$$50-60$$32$$55$$1$$32$$60-70$$f$$65$$2$$2f$$70-80$$8$$75$$3$$24$$80-90$$2$$85$$4$$8$$90-100$$2$$95$$5$$10$Total$\sum f_i = 185 + f$--$\sum f_i u_i = 2f - 55$Here,$A = 45$ and $c = 10$.Given $\bar{x} = 43.75$.$43.75 = 45 + \frac{2f - 55}{185 + f} 	imes 10$$-1.25 = \frac{10(2f - 55)}{185 + f}$$-1.25(185 + f) = 20f - 550$$-231.25 - 1.25f = 20f - 550$$550 - 231.25 = 20f + 1.25f$$318.75 = 21.25f$$f = \frac{318.75}{21.25} = 15$.Thus,the missing frequency $f = 15$.

Number of pages written per day	$16-18$	$19-21$	$22-24$	$25-27$	$28-30$
Number of days	$1$	$3$	$4$	$9$	$13$

The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
Frequency $8$ $4$ $20$ $45$ $64$ $32$ $f$ $8$ $2$ $2$

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If $Z = 36.8$ and $M = 33.6$,then $\bar{x} = \ldots \ldots \ldots \ldots .$

Calculate the mean of the following frequency distribution:

Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Frequency $12$ $16$ $8$ $6$ $8$

The following table gives the number of pages written by Sarika for completing her own book over $30$ days:

Number of pages written per day $16-18$ $19-21$ $22-24$ $25-27$ $28-30$

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Find the mean number of pages written per day.

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Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$8$	$4$	$20$	$45$	$64$	$32$	$f$	$8$	$2$	$2$

The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.Class$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$$60-70$$70-80$$80-90$$90-100$Frequency$8$$4$$20$$45$$64$$32$$f$$8$$2$$2$