The mileage $(km/l)$ of $50$ cars of the same model was tested by a manufacturer and details are tabulated as given below:
Mileage $(km/l)$ $10-12$ $12-14$ $14-16$ $16-18$ Number of cars $7$ $12$ $18$ $13$
Find the mean mileage.
The manufacturer claimed that the mileage of the model was $16 \, km/l$. Do you agree with this claim?
| Mileage $(km/l)$ | $10-12$ | $12-14$ | $14-16$ | $16-18$ |
| Number of cars | $7$ | $12$ | $18$ | $13$ |
Find the mean mileage.
The manufacturer claimed that the mileage of the model was $16 \, km/l$. Do you agree with this claim?
(A)
Here,$\Sigma f_i = 50$ and $\Sigma f_i x_i = 724$.
Mean $\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{724}{50} = 14.48$.
Hence,the mean mileage is $14.48 \, km/l$.
No,$I$ do not agree with the manufacturer's claim,as the calculated mean mileage $(14.48 \, km/l)$ is significantly less than the claimed $16 \, km/l$.
| Mileage $(km/l)$ | Class marks $(x_i)$ | Number of cars $(f_i)$ | $f_i x_i$ |
| $10-12$ | $11$ | $7$ | $77$ |
| $12-14$ | $13$ | $12$ | $156$ |
| $14-16$ | $15$ | $18$ | $270$ |
| $16-18$ | $17$ | $13$ | $221$ |
| Total | - | $\Sigma f_i = 50$ | $\Sigma f_i x_i = 724$ |
Here,$\Sigma f_i = 50$ and $\Sigma f_i x_i = 724$.
Mean $\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{724}{50} = 14.48$.
Hence,the mean mileage is $14.48 \, km/l$.
No,$I$ do not agree with the manufacturer's claim,as the calculated mean mileage $(14.48 \, km/l)$ is significantly less than the claimed $16 \, km/l$.
Explore More
Similar Questions
The median of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ Frequency $5$ $x$ $20$ $15$ $y$ $5$
| Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ |
| Frequency | $5$ | $x$ | $20$ | $15$ | $y$ | $5$ |
Medium
View SolutionThe following are the ages of $300$ patients getting medical treatment in a hospital on a particular day:
Age (in years) $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ Number of patients $60$ $42$ $55$ $70$ $53$ $20$
Form:
$(i)$ Less than type cumulative frequency distribution.
$(ii)$ More than type cumulative frequency distribution.
| Age (in years) | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ |
| Number of patients | $60$ | $42$ | $55$ | $70$ | $53$ | $20$ |
Form:
$(i)$ Less than type cumulative frequency distribution.
$(ii)$ More than type cumulative frequency distribution.
Medium
View SolutionIf $x_{i}$ are the midpoints of the class intervals of grouped data,$f_{i}$ are the corresponding frequencies,and $\bar{x}$ is the mean,then $\sum (f_{i} x_{i} - f_{i} \bar{x})$ is equal to
Easy
View SolutionIf $Z - M = 4$,then $M - \bar{x} = \dots$
Medium
View SolutionIn the formula $\bar{x} = A + \frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}}$,$d_{i} =$ .........
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo