Download App

Mean, Median, Mode of Grouped Data — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMean, Median, Mode of Grouped Data5 Marks
Question
Find the mean of the following frequency distribution using step-deviation method.
Class
0-10
10-20
20-30
30-40
40-50
Frequency
7
10
15
8
10
✓

Answer

Class interval
Frequency $f_i$
Mid-value $x_i$
$d_i = x_i − 25$
$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{A}}{\text{h}}=\frac{\text{x}_\text{i}-25}{10}$
$f_i \times u_i$
0-10
7
5
−20
−2
−14
10-20
10
15
−10
−1
−10
20-30
15
25
0
0
0
30-40
8
35
10
1
8
40-50
10
45
20
2
20
 
$\sum\text{f}_\text{i}=50$
 
 
 
$\sum\text{f}_\text{i}\text{u}_\text{i}=4$
Thus, $\text{A}=25,\ \text{h}=10,\ \sum\text{f}_\text{i}=50$ and $\sum\text{f}_\text{i}\text{u}_\text{i}=4$
Mean $=\text{A}+\Big\{\text{h}\times\frac{\sum\text{f}_\text{i}\text{u}_\text{i}}{\sum\text{f}_\text{i}}\Big\}$
$25+\Big\{10\times\frac{4}{50}\Big\}$
$=25.08$
$=25.8$

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 "5 Marks Questions" from Mean, Median, Mode of Grouped Data→Mean, Median, Mode of Grouped Data — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Solve the following quadratic equations by factorization:
$\text{x}^2-\big(\sqrt{2}+1\big)\text{x}+\sqrt{2}=0$
→
There are two classrooms A and B. If 10 students are sent from A to B, the number of students in each room becomes the same. If 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in each room.
→
The angle of elevation of the top of tower at a distance of 120m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. $\big[\text{Use}\sqrt{3}=1.732\big]$
→
Short-Answer Question:
If $\alpha$ and $\beta$ are the zeroes of a polynomial $f(x) = x^2 - 5x + k$, such that $\alpha-\beta=1$ find the value of k.
→
How many spherical lead shots each of diameter 4.2cm can be obtained from a solid rectangular lead piece with dimensions 66cm, 42cm and 21cm.
→
The height of 50 girls of class X of a school are recorded as follows:
Height (in cm)
135-140
140-145
145-150
150-155
155-160
160-165
Number of girls
5
8
9
12
14
2
Draw a 'more than type' ogive for the above data.
→
Solve the following quadratic equations by factorization:
$\frac{5+\text{x}}{5-\text{x}}-\frac{5-\text{x}}{5+\text{x}}=3\frac{3}{4},$ $\text{x}\neq5,-5$
→
The sum of the $4^{\text {th }}$ and the $8^{\text {th }}$ term of an AP is 24 and the sum of its $6^{\text {th }}$ and $10^{\text {th }}$ terms is 44 . Find the sum of its first 10 terms.
→
The adjacent sides of a parallelogram ABCD measure 34cm and 20cm, and the diagonal AC measures 42cm. Find the area of the parallelogram.
→
Find the sum of the odd numbers between 0 and 50.
→