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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	$4-7$	$8-11$	$12-15$	$16-19$
Frequency	$5$	$4$	$9$	$10$

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$12$	$16$	$8$	$6$	$8$

Class	$15-35$	$35-55$	$55-75$	$75-95$	$95-115$
Frequency	$17$	$f_1$	$32$	$f_2$	$19$

Similar Questions

Midpoint (Midvalue) of the class $15-30$ is ........

Calculate the mean of the following data:

Class $4-7$ $8-11$ $12-15$ $16-19$

Frequency $5$ $4$ $9$ $10$

Calculate the mean of the following frequency distribution:

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

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

For a given frequency distribution,$n=200$,$\Sigma f_{i} d_{i}=0$ and $A=25$. Then,$\bar{x}=\ldots \ldots \ldots \ldots$

The mean of the following frequency distribution is $65$ and the total frequency is $100$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class $15-35$ $35-55$ $55-75$ $75-95$ $95-115$

Frequency $17$ $f_1$ $32$ $f_2$ $19$

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