Statement $(I)$: The range of the ungrouped data does not change even if certain intermediate observations are removed.
Statement $(II)$: The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency.
Statement $(III)$: For a grouped data,range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.
Statement $(II)$: The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency.
Statement $(III)$: For a grouped data,range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.
- AStatements $I$ and $II$ are true but statement $III$ is false
- BStatements $II$ and $III$ are true but statement $I$ is false
- CStatements $III$ and $I$ are true but statement $II$ is false
- DStatements $I$,$II$ and $III$ are true
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Similar Questions
There are $60$ students in a class. The following is the frequency distribution of the marks obtained by the students in a test:
$\begin{array}{|l|l|l|l|l|l|l|} \hline \text{Marks} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{Frequency} & x-2 & x & x^2 & (x+1)^2 & 2x & x+1 \\ \hline \end{array}$
where $x$ is a positive integer. Determine the mean and standard deviation of the marks.
$\begin{array}{|l|l|l|l|l|l|l|} \hline \text{Marks} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{Frequency} & x-2 & x & x^2 & (x+1)^2 & 2x & x+1 \\ \hline \end{array}$
where $x$ is a positive integer. Determine the mean and standard deviation of the marks.
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View Solution$A$ pie chart is to be drawn for representing the following data. The value of the central angle for food and clothing would be...$^o$
Items of expenditure Number of families $Education$ $150$ $Food and clothing$ $400$ $House rent$ $40$ $Electricity$ $250$ $Miscellaneous$ $160$
| Items of expenditure | Number of families |
| $Education$ | $150$ |
| $Food and clothing$ | $400$ |
| $House rent$ | $40$ |
| $Electricity$ | $250$ |
| $Miscellaneous$ | $160$ |
Difficult
View SolutionThe coefficients of variation of two distributions are $60$ and $70$. The standard deviations are $21$ and $16$ respectively. Find their means.
Consider the following frequency distribution:
Class: $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ Freq: $\alpha$ $110$ $54$ $30$ $\beta$
If the sum of all frequencies is $584$ and the median is $45$,then $|\alpha-\beta|$ is equal to $.....$
| Class: | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ |
| Freq: | $\alpha$ | $110$ | $54$ | $30$ | $\beta$ |
If the sum of all frequencies is $584$ and the median is $45$,then $|\alpha-\beta|$ is equal to $.....$
DifficultJEE MAIN 2021
View SolutionThe coefficients of variation of two distributions are $60$ and $70$,and their standard deviations are $21$ and $16$,respectively. What are their arithmetic means?
Medium
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