12 Views

Question : Calculate the mean from the following table.

Scores Frequencies
0-10 2
10-20 4
20-30 12
30-40 21
40-50 6
50-60 3
60-70 2

Option 1: 33.4

Option 2: 32.6

Option 3: 35.8

Option 4: 34.2


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 33.4


Solution : The formula for the mean ($X$) using the method of assumed mean is:
$X = A + \frac{\sum fd}{\sum f}$ where $A$ is assumed mean, $f$ is frequency, and $d$ is deviation from mean.
The assumed mean ($A$) is usually taken as the midpoint of the middle class. In this case, it's 35.
The midpoints of the score ranges are 5, 15, 25, 35, 45, 55, and 65.
The frequencies are 2, 4, 12, 21, 6, 3, and 2.

Midpoint ($x$) Frequency($f$) Deviation ($d = x - A$) $fd$
5 2 –30 –60
15 4 –20 –80
25 12 –10 –120
35 21 0 0
45 6 10 60
55 3 20 60
65 2 30 60
$\sum f$ = 50 $\sum fd$ = –80

The formula for the mean ($X$) using the method of assumed mean is:
$X = A + \frac{\sum fd}{\sum f}$
⇒ $X = 35 + \frac{-80}{50} = 33.4$
Hence, the correct answer is 33.4.

Know More About

Related Questions

Question : The total number of teachers in different subjects and the respective percentage of females among them in a school are given in the following table. Study the table and answer the following question.

2 Views
TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books