You visited us 1 times! Enjoying our articles? Unlock Full Access!

Mean

The mean of f...

Question

The mean of following frequency table is $50.$
If the total of frequency is $120.$ Then the missing frequencies $f_{1}, f_{2}$ are respectively
$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}$

24, 28

No worries! We‘ve got your back. Try BYJU‘S free classes today!

28, 24

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

25, 27

No worries! We‘ve got your back. Try BYJU‘S free classes today!

27, 25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $28, 24$
Given : $\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}$

Total frequency $= 120$ , then
$17 + f_{1} + 32 + f_{2} + 19 = 120 \Rightarrow f_{1} + f_{2} = 52 \dots (1)$
We know the mean
$¯ ¯ ¯ x = \sum \frac{f_{i} x_{i}}{N} x_{1} = \frac{x_{i} + x_{f}}{2} = \frac{0 + 20}{2} = 10 x_{2} = \frac{x_{i} + x_{f}}{2} = \frac{20 + 40}{2} = 30 x_{3} = \frac{x_{i} + x_{f}}{2} = \frac{40 + 60}{2} = 50 x_{4} = \frac{x_{i} + x_{f}}{2} = \frac{60 + 80}{2} = 70 x_{5} = \frac{x_{i} + x_{f}}{2} = \frac{80 + 100}{2} = 90$
Therefore,
$¯ ¯ ¯ x = \frac{f_{1} x_{1} + f_{2} x_{2} + f_{3} x_{3} + f_{4} x_{4} + f_{5} x_{5}}{N} \Rightarrow 50 = \frac{17 \times 10 + f_{1} \times 30 + 32 \times 50 + f_{2} \times 70 + 19 \times 90}{120} \Rightarrow 6000 = 170 + 30 f_{1} + 1600 + 70 f_{2} + 1710 \Rightarrow 6000 = 30 f_{1} + 70 f_{2} + 3480 \Rightarrow 2520 = 30 f_{1} + 70 f_{2} \Rightarrow 3 f_{1} + 7 f_{2} = 252 \dots (2)$

Solving equation s $(1)$ and $(2)$ , we get
$f_{1} = 28, f_{2} = 24$

Suggest Corrections

Similar questions

Q. The mean of following frequency table is

50.

If the total of frequency is

120.

Then the missing frequencies

f_{1}, f_{2}

are respectively

\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}

Q. The mean of the following frequency distribution of

62.8

and the sum of all frequencies is

50

Compute the sum of missing frequencies

f_{1}

and

f_{2}

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	$5$	$f_{1}$	$10$	$f_{2}$	$7$	$8$

Q. The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies

f_{1}

and

f_{2}

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120	Total
Frequency	5	$f_{1}$	10	$f_{2}$	7	8	50

Question 8
The mean of the following frequency distribution is 50 but the frequencies $f_{1}$ and $f_{2}$ in classes 20-40 and 60-80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.
$\begin{matrix} C l a s s & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 F r e q u e n c y & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}$

Q. The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f₁ and f₂.

Class:	0−20	20−40	40−60	60−80	80−100	100−120
Frequency:	5	f₁	10	f₂	7	9

Join BYJU'S Learning Program

Explore more

Mean

Standard XII Mathematics

Join BYJU'S Learning Program

The mean of following frequency table is 50. If the total of frequency is 120. Then the missing frequencies f1,f2 are respectively Class0−2020−4040−6060−8080−100Frequency17f132f219

The mean of following frequency table is $50.$
If the total of frequency is $120.$ Then the missing frequencies $f_{1}, f_{2}$ are respectively
$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}$