The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.
(N/A) No,this is not a correct statement. The median of ungrouped data and the median calculated from grouped data are not always the same. This is because the formula used for calculating the median of grouped data,$\text{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} \right) \times h$,is based on the assumption that the observations within each class interval are uniformly distributed. In reality,the actual distribution of data within classes may not be uniform,leading to a slight difference between the two values.
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Similar Questions
In the formula $\bar{x} = A + \frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}}$ for the mean,$d_{i} = \dots$
Easy
View SolutionThe modal class of the following frequency distribution is ........
Class $4-8$ $8-12$ $12-16$ $16-20$ $20-24$ $24-28$ Frequency $9$ $8$ $12$ $7$ $15$ $1$
| Class | $4-8$ | $8-12$ | $12-16$ | $16-20$ | $20-24$ | $24-28$ |
| Frequency | $9$ | $8$ | $12$ | $7$ | $15$ | $1$ |
Easy
View SolutionIn a frequency distribution,the modal class is $70-85$ with frequency $25$. The frequencies of the classes succeeding and preceding the modal class are $20$ and $8$ respectively. Then,the values of $f_{0}, f_{1}$ and $f_{2}$ are respectively.
Medium
View SolutionFor a given frequency distribution,assumed mean $A = 25$,$\Sigma f_{i} d_{i} = 120$ and $\Sigma f_{i} = 140$. Then,the mean $\bar{x} = \dots$
Easy
View SolutionFind the median of the following frequency distribution:
Class Frequency $(f)$ $110-120$ $6$ $120-130$ $25$ $130-140$ $48$ $140-150$ $72$ $150-160$ $116$ $160-170$ $60$ $170-180$ $38$ $180-190$ $22$ $190-200$ $3$
| Class | Frequency $(f)$ |
|---|---|
| $110-120$ | $6$ |
| $120-130$ | $25$ |
| $130-140$ | $48$ |
| $140-150$ | $72$ |
| $150-160$ | $116$ |
| $160-170$ | $60$ |
| $170-180$ | $38$ |
| $180-190$ | $22$ |
| $190-200$ | $3$ |
Difficult
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