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(A) From the given data, it can be observed that the maximum class frequency is $20,$ which belongs to the $40-50$ class interval.Therefore, the modal

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$44.7$

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(A) From the given data, it can be observed that the maximum class frequency is $20,$ which belongs to the $40-50$ class interval.Therefore, the modal class $= 40-50$.Lower limit $(l)$ of the modal class $= 40$.Frequency $(f_1)$ of the modal class $= 20$.Frequency $(f_0)$ of the class preceding the modal class $= 12$.Frequency $(f_2)$ of the class succeeding the modal class $= 11$.Class size $(h) = 10$.Using the mode formula: $	ext{Mode} = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} ight) 	imes h$.$	ext{Mode} = 40 + \left( \frac{20 - 12}{2(20) - 12 - 11} ight) 	imes 10$.$	ext{Mode} = 40 + \left( \frac{8}{40 - 23} ight) 	imes 10$.$	ext{Mode} = 40 + \left( \frac{8}{17} ight) 	imes 10$.$	ext{Mode} = 40 + \frac{80}{17}$.$	ext{Mode} = 40 + 4.705 \approx 44.7$.Therefore, the mode of this data is $44.7$ cars.

Number of cars	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$7$	$14$	$13$	$12$	$20$	$11$	$15$	$8$

Lifetimes (in hours)	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$
Frequency	$10$	$35$	$52$	$61$	$38$	$29$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$4$	$7$	$x$	$18$	$15$	$8$	$7$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$6$	$8$	$17$	$x$	$42$	$30$	$y$	$8$

Marks	Number of students
Below $10$	$3$
Below $20$	$12$
Below $30$	$27$
Below $40$	$57$
Below $50$	$75$
Below $60$	$80$

Similar Questions

The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:
Lifetimes (in hours) $0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$
Frequency $10$ $35$ $52$ $61$ $38$ $29$

Determine the modal lifetimes of the components.

The mode of the following frequency distribution is $37$. Find the missing frequency $x$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$
Frequency $4$ $7$ $x$ $18$ $15$ $8$ $7$

The mode of the following frequency distribution is $46$ and the total frequency is $150$. Find the missing frequencies $x$ and $y$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

Frequency $6$ $8$ $17$ $x$ $42$ $30$ $y$ $8$

For the following distribution,the modal class is:

Marks Number of students

Below $10$ $3$

Below $20$ $12$

Below $30$ $27$

Below $40$ $57$

Below $50$ $75$

Below $60$ $80$

In the formula $Z = l + \left( \frac{f_{1} - f_{0}}{2f_{1} - f_{0} - f_{2}} \right) \times c$,$f_{1}$ represents:

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$A$ student noted the number of cars passing through a spot on a road for $100$ periods each of $3\, \text{minutes}$ and summarized it in the table given below. Find the mode of the data:Number of cars$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$$60-70$$70-80$Frequency$7$$14$$13$$12$$20$$11$$15$$8$

Similar Questions

The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:Lifetimes (in hours)$0-20$$20-40$$40-60$$60-80$$80-100$$100-120$Frequency$10$$35$$52$$61$$38$$29$Determine the modal lifetimes of the components.

The mode of the following frequency distribution is $37$. Find the missing frequency $x$.Class$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$$60-70$Frequency$4$$7$$x$$18$$15$$8$$7$

The mode of the following frequency distribution is $46$ and the total frequency is $150$. Find the missing frequencies $x$ and $y$. Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ Frequency $6$ $8$ $17$ $x$ $42$ $30$ $y$ $8$

For the following distribution,the modal class is: Marks Number of students Below $10$ $3$ Below $20$ $12$ Below $30$ $27$ Below $40$ $57$ Below $50$ $75$ Below $60$ $80$