Consider a small unit of a factory where there are $5$ employees: a supervisor and four labourers. The labourers draw a salary of $Rs. 5,000$ per month each,while the supervisor gets $Rs. 15,000$ per month. Calculate the mean,median,and mode of the salaries of this unit of the factory.
(A) Mean = $\frac{5000+5000+5000+5000+15000}{5} = \frac{35000}{5} = 7000$.
So,the mean salary is $Rs. 7000$ per month.
To obtain the median,we arrange the salaries in ascending order:
$5000, 5000, 5000, 5000, 15000$.
Since the number of employees in the factory is $5$,the median is given by the $\left(\frac{5+1}{2}\right)^{th} = 3^{rd}$ observation.
Therefore,the median is $Rs. 5000$ per month.
To find the mode of the salaries,we observe that $5000$ occurs the maximum number of times in the data. So,the modal salary is $Rs. 5000$ per month.
Comparing the three measures of central tendency,we see that the mean salary of $Rs. 7000$ does not give an accurate estimate of the wages of the majority,while the median and mode of $Rs. 5000$ represent the data more effectively. Extreme values in the data affect the mean,which is a weakness of this measure.
So,the mean salary is $Rs. 7000$ per month.
To obtain the median,we arrange the salaries in ascending order:
$5000, 5000, 5000, 5000, 15000$.
Since the number of employees in the factory is $5$,the median is given by the $\left(\frac{5+1}{2}\right)^{th} = 3^{rd}$ observation.
Therefore,the median is $Rs. 5000$ per month.
To find the mode of the salaries,we observe that $5000$ occurs the maximum number of times in the data. So,the modal salary is $Rs. 5000$ per month.
Comparing the three measures of central tendency,we see that the mean salary of $Rs. 7000$ does not give an accurate estimate of the wages of the majority,while the median and mode of $Rs. 5000$ represent the data more effectively. Extreme values in the data affect the mean,which is a weakness of this measure.
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Similar Questions
Consider the marks,out of $100$,obtained by $51$ students of a class in a test,given in the table below. Draw a frequency polygon corresponding to this frequency distribution table.
Marks Number of students $0-10$ $5$ $10-20$ $10$ $20-30$ $4$ $30-40$ $6$ $40-50$ $7$ $50-60$ $3$ $60-70$ $2$ $70-80$ $2$ $80-90$ $3$ $90-100$ $9$ Total $51$
| Marks | Number of students |
| $0-10$ | $5$ |
| $10-20$ | $10$ |
| $20-30$ | $4$ |
| $30-40$ | $6$ |
| $40-50$ | $7$ |
| $50-60$ | $3$ |
| $60-70$ | $2$ |
| $70-80$ | $2$ |
| $80-90$ | $3$ |
| $90-100$ | $9$ |
| Total | $51$ |
Medium
View Solution$A$ family with a monthly income of $20,000$ had planned the following expenditures per month under various heads:
Heads Expenditure (in thousand rupees) Grocery $4$ Rent $5$ Education of children $5$ Medicine $2$ Fuel $2$ Entertainment $1$ Miscellaneous $1$
Draw a bar graph for the data above.
| Heads | Expenditure (in thousand rupees) |
|---|---|
| Grocery | $4$ |
| Rent | $5$ |
| Education of children | $5$ |
| Medicine | $2$ |
| Fuel | $2$ |
| Entertainment | $1$ |
| Miscellaneous | $1$ |
Draw a bar graph for the data above.
Medium
View SolutionFind the mean salary of $60$ workers of a factory from the following table:
Salary (in Rs.) Number of workers $3000$ $16$ $4000$ $12$ $5000$ $10$ $6000$ $8$ $7000$ $6$ $8000$ $4$ $9000$ $3$ $10000$ $1$ Total $60$
| Salary (in Rs.) | Number of workers |
| $3000$ | $16$ |
| $4000$ | $12$ |
| $5000$ | $10$ |
| $6000$ | $8$ |
| $7000$ | $6$ |
| $8000$ | $4$ |
| $9000$ | $3$ |
| $10000$ | $1$ |
| Total | $60$ |
Difficult
View Solution$A$ random survey of the number of children of various age groups playing in a park was found as follows:
Age (in years) Number of children $1-2$ $5$ $2-3$ $3$ $3-5$ $6$ $5-7$ $12$ $7-10$ $9$ $10-15$ $10$ $15-17$ $4$
Draw a histogram to represent the data above.
| Age (in years) | Number of children |
| $1-2$ | $5$ |
| $2-3$ | $3$ |
| $3-5$ | $6$ |
| $5-7$ | $12$ |
| $7-10$ | $9$ |
| $10-15$ | $10$ |
| $15-17$ | $4$ |
Draw a histogram to represent the data above.
Medium
View SolutionThe lengths of $40$ leaves of a plant are measured correct to one millimetre,and the obtained data is represented in the following table:
Length (in $mm$) Number of leaves $118-126$ $3$ $127-135$ $5$ $136-144$ $9$ $145-153$ $12$ $154-162$ $5$ $163-171$ $4$ $172-180$ $2$
$(i)$ Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
$(ii)$ Is there any other suitable graphical representation for the same data?
$(iii)$ Is it correct to conclude that the maximum number of leaves are $153 \, mm$ long? Why?
| Length (in $mm$) | Number of leaves |
| $118-126$ | $3$ |
| $127-135$ | $5$ |
| $136-144$ | $9$ |
| $145-153$ | $12$ |
| $154-162$ | $5$ |
| $163-171$ | $4$ |
| $172-180$ | $2$ |
$(i)$ Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
$(ii)$ Is there any other suitable graphical representation for the same data?
$(iii)$ Is it correct to conclude that the maximum number of leaves are $153 \, mm$ long? Why?
Medium
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