The mean of the following frequency distribut | vedclass

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(D) Given total frequency $N = 60$.Sum of frequencies: $6 + f_1 + 20 + 15 + f_2 + 4 = 60$$45 + f_1 + f_2 = 60 \implies f_1 + f_2 = 15$  ---(Equation $

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$8, 7$

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(D) Given total frequency $N = 60$.Sum of frequencies: $6 + f_1 + 20 + 15 + f_2 + 4 = 60$$45 + f_1 + f_2 = 60 \implies f_1 + f_2 = 15$  ---(Equation $1$)Calculate midpoint $(x_i)$ and $f_i x_i$:Class $0-10$: $x_i = 5, f_i x_i = 30$Class $10-20$: $x_i = 15, f_i x_i = 15f_1$Class $20-30$: $x_i = 25, f_i x_i = 500$Class $30-40$: $x_i = 35, f_i x_i = 525$Class $40-50$: $x_i = 45, f_i x_i = 45f_2$Class $50-60$: $x_i = 55, f_i x_i = 220$Sum $\sum f_i x_i = 30 + 15f_1 + 500 + 525 + 45f_2 + 220 = 1275 + 15f_1 + 45f_2$Mean $\bar{x} = \frac{\sum f_i x_i}{N} = 28.5$$\frac{1275 + 15f_1 + 45f_2}{60} = 28.5$$1275 + 15f_1 + 45f_2 = 1710$$15f_1 + 45f_2 = 435$Divide by $15$: $f_1 + 3f_2 = 29$ ---(Equation $2$)Subtract Equation $1$ from Equation $2$:$(f_1 + 3f_2) - (f_1 + f_2) = 29 - 15$$2f_2 = 14 \implies f_2 = 7$Substitute $f_2 = 7$ in Equation $1$: $f_1 + 7 = 15 \implies f_1 = 8$.Thus,$f_1 = 8$ and $f_2 = 7$.

Number of seats	$100-104$	$104-108$	$108-112$	$112-116$	$116-120$
Frequency	$15$	$20$	$32$	$18$	$15$

Mileage $(km/l)$	$10-12$	$12-14$	$14-16$	$16-18$
Number of cars	$7$	$12$	$18$	$13$

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

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$

The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$.

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

Frequency $6$ $f_1$ $20$ $15$ $f_2$ $4$

Similar Questions

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

An aircraft has $120$ passenger seats. The number of seats occupied during $100$ flights is given in the following table:

Number of seats $100-104$ $104-108$ $108-112$ $112-116$ $116-120$

Frequency $15$ $20$ $32$ $18$ $15$

Determine the mean number of seats occupied over the flights. (in $.92$)

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 $16-18$ $19-21$ $22-24$ $25-27$ $28-30$

Number of days $1$ $3$ $4$ $9$ $13$

Find the mean number of pages written per day.

The median of the following frequency distribution is $46$ and the total frequency is $230$. Find the missing frequencies $x$ and $y$.

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

Frequency $12$ $30$ $x$ $65$ $y$ $25$ $18$

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Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$6$	$f_1$	$20$	$15$	$f_2$	$4$

The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$. Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ Frequency $6$ $f_1$ $20$ $15$ $f_2$ $4$