Is it true to say that the mean,mode,and median of grouped data will always be different? Justify your answer.
(N/A) No,it is not true to say that the mean,mode,and median of grouped data will always be different.
These three measures of central tendency can be the same depending on the nature of the data.
For example,in a perfectly symmetrical distribution (such as a normal distribution),the mean,median,and mode are equal.
Therefore,the values of these three measures depend entirely on the distribution of the data.
These three measures of central tendency can be the same depending on the nature of the data.
For example,in a perfectly symmetrical distribution (such as a normal distribution),the mean,median,and mode are equal.
Therefore,the values of these three measures depend entirely on the distribution of the data.
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Similar Questions
If $Z - M = 4$,then $M - \bar{x} = \dots$
Medium
View SolutionConsider the following frequency distribution of the heights of $60$ students of a class:
Height (in $cm$) Number of students $150-155$ $15$ $155-160$ $13$ $160-165$ $10$ $165-170$ $8$ $170-175$ $9$ $175-180$ $5$
The sum of the lower limit of the modal class and upper limit of the median class is:
| Height (in $cm$) | Number of students |
| $150-155$ | $15$ |
| $155-160$ | $13$ |
| $160-165$ | $10$ |
| $165-170$ | $8$ |
| $170-175$ | $9$ |
| $175-180$ | $5$ |
The sum of the lower limit of the modal class and upper limit of the median class is:
Easy
View SolutionForm the frequency distribution table from the following cumulative frequency data:
Marks (out of $90$) Number of candidates More than or equal to $80$ $4$ More than or equal to $70$ $6$ More than or equal to $60$ $11$ More than or equal to $50$ $17$ More than or equal to $40$ $23$ More than or equal to $30$ $27$ More than or equal to $20$ $30$ More than or equal to $10$ $32$ More than or equal to $0$ $34$
| Marks (out of $90$) | Number of candidates |
| More than or equal to $80$ | $4$ |
| More than or equal to $70$ | $6$ |
| More than or equal to $60$ | $11$ |
| More than or equal to $50$ | $17$ |
| More than or equal to $40$ | $23$ |
| More than or equal to $30$ | $27$ |
| More than or equal to $20$ | $30$ |
| More than or equal to $10$ | $32$ |
| More than or equal to $0$ | $34$ |
Medium
View SolutionThe mean of the following data is $26.5$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequency $6$ $x$ $17$ $y$ $8$
| Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Frequency | $6$ | $x$ | $17$ | $y$ | $8$ |
Medium
View SolutionFor a given frequency distribution,$A = 200$,$\Sigma f_{i} = 45$,$\Sigma f_{i} u_{i} = -216$ and $c = 10$. Then,mean $\bar{x} = \dots$
Easy
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