Download App

Statistics — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsStatistics4 Marks
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→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Draw circles with centres A, B and C each of radius 3 cm, such that each circle touches the other two circles.
→
Evaluate the following:
If A = 60° and B = 30°, verify that:
$\tan(\text{A}-\text{B})=\frac{\tan\text{A}-\tan\text{B}}{1+\tan\text{A}\tan\text{B}}$
→
Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and y-axis. Calculate the area of the triangle so formed.
→
If the roots of the quadratic equation $a x^2+c x+c=0$ are in the ratio $p : q$, then show that
$\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{c}{a}}=0$
→
Prove the following identities:
$\frac{\sin\theta}{(\cot\theta+\text{cosec }\theta)}-\frac{\sin\theta}{(\cot\theta-\text{cosec }\theta)}=2$
→
Prepare Business to Business (B2B) Tax Invoice as per the details given below. name of the supplier, address, Date etc. as per your choice.
Supplier - Name, Address, State, GSTIN, Invoice No., Date
Recipient - Name, Address, State, GSTIN,
Items :
(1) Pencil boxes 100, HSN - 3924, Rate - Rs. 20, GST 12%
(2) Jigsaw Puzzles 50, HSN 9503, Rate - Rs. 100 GST 12%.
→
Solve the following quadratic equations by factorization:
$\text{x}^2-\big(\sqrt{2}+1\big)\text{x}+\sqrt{2}=0$
→
Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is 1/6. Find their present ages.
→
From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60. If the lighthouse is 90 m, then find how far is that ship from the lighthouse? $(\sqrt{3}=1.73)$
→
In the given figure, MN || BC and AM : MB = 1 : 2
Find $\frac{\text{area}(\triangle\text{AMN})}{\text{area}(\triangle\text{ABC})}.$
→