Calculate the missing frequency from the following distribution, … - Vidyadip

Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution

Age in years	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
No. of persons	$5$	$25$	$?$	$18$	$7$

✓

Answer

Let the frequency of the class $20-30$ be $f_1.$ It is given that median is $35$ which lies
in the class $20-30.$ So $20-30$ is the median class.
Now, lower limit of median class $(l) = 20$
Height of the class $(h) = 10$
Frequency of median class $= (f) = f_1$
Cumulative frequency of preceding median class $(F) = 5 + 25$
Total frequency $(N) =55 + f_1$
Formula to be used to calculate median,
$=\text{l}+\bigg(\frac{\frac{\text{N}}{2}-\text{F}}{\text{f}}\bigg)\text{(h)}$
Where,
$l-$ Lower limit of median class
$h-$ Height of the class
$f-$ Frequency of median class
$F-$ Cumulative frequency of preceding median class
$N-$ Total frequency
Put the values in the above,
$=24=20+\Bigg(\frac{\frac{\text{(55}+\text{f}_1)}{2}-30}{\text{f}_1}\Bigg)(10)$
$\frac{4}{10}=\frac{55+\text{f}_1-60}{2\text{f}_1}$
$2\ \text{f}_1=50$
$\text{f}_1=25$
Hence, the required frequency is $25. $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Statistics→Statistics — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Find the area of a triangle whose vertices are,
$(\text{at}_1^2, 2\text{at}_1), (\text{at}_2^2, 2\text{at}_2)$ and $(\text{at}_3^2, 2\text{at}_3).$

A round table cover has six equal designs as shown in figure. If the radius of the cover is $28\ cm,$ find the cost of making the designs at the rate of $₹\ 0.35\ per\ cm^2. ($use $\sqrt 3 = 1.7)$

Show that the points $A(1,-2), B(3,6), C(5,10)$ and $D(3,2)$ are the vertices of a parallelogram.

Solve the following quadratic equations by factorization:
$\frac{5+\text{x}}{5-\text{x}}-\frac{5-\text{x}}{5+\text{x}}=3\frac{3}{4},$ $\text{x}\neq5,-5$

Equal circle with centres $O$ and $O'$ touches each other at $X. OO'$ produced to meet a circle with center $O'$ at A. $AC$ is a tangent to the circle whose centre is $O. O'D$ is
perpendicular to AC. Find the value of $\frac{\text{DO'}}{\text{CO}}.$

Solve the following systems of equations:

$152x - 378y = −74,$

$-378x + 152y = -604.$

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:
$\text{g(x)}=\text{a(x}^2+1)-\text{x(a}^2+1)$

The sum of the squares of two consecutive positive even numbers is $452$. Find the numbers.

The perimeter of a rectangular field is $82\ m$ and its area is $400m^2$. Find the breadth of the rectangle.

The sum of a two-digit number and the number formed by reversing the order of digit is $66$. If the two digits differ by $2$, find the number. How many such numbers are there?