The mean of ungrouped data and the mean calculated when the same data is grouped are always the same. Do you agree with this statement? Give reason for your answer.
(B) The statement is not true.
When we calculate the mean of grouped data,we assume that the frequency of each class is centered at the mid-point of that class.
In reality,the individual observations within a class are rarely distributed exactly at the mid-point.
Therefore,the mean calculated from grouped data is an approximation,and it is rarely the same as the mean calculated from the original ungrouped data.
When we calculate the mean of grouped data,we assume that the frequency of each class is centered at the mid-point of that class.
In reality,the individual observations within a class are rarely distributed exactly at the mid-point.
Therefore,the mean calculated from grouped data is an approximation,and it is rarely the same as the mean calculated from the original ungrouped data.
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Similar Questions
For the following distribution,the modal class is:
Marks Number of students Below $10$ $3$ Below $20$ $12$ Below $30$ $27$ Below $40$ $57$ Below $50$ $75$ Below $60$ $80$
| Marks | Number of students |
| Below $10$ | $3$ |
| Below $20$ | $12$ |
| Below $30$ | $27$ |
| Below $40$ | $57$ |
| Below $50$ | $75$ |
| Below $60$ | $80$ |
Easy
View SolutionAn aircraft has $120$ passenger seats. The number of seats occupied during $100$ flights is given in the following table:
Number of seats $100-104$ $104-108$ $108-112$ $112-116$ $116-120$ Frequency $15$ $20$ $32$ $18$ $15$
Determine the mean number of seats occupied over the flights. (in $.92$)
| Number of seats | $100-104$ | $104-108$ | $108-112$ | $112-116$ | $116-120$ |
| Frequency | $15$ | $20$ | $32$ | $18$ | $15$ |
Determine the mean number of seats occupied over the flights. (in $.92$)
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 SolutionThe monthly income of $100$ families is given as follows:
Income (in $Rs.$) Number of families $0-5000$ $8$ $5000-10000$ $26$ $10000-15000$ $41$ $15000-20000$ $16$ $20000-25000$ $3$ $25000-30000$ $3$ $30000-35000$ $2$ $35000-40000$ $1$
Calculate the modal income (in $Rs.$).
| Income (in $Rs.$) | Number of families |
| $0-5000$ | $8$ |
| $5000-10000$ | $26$ |
| $10000-15000$ | $41$ |
| $15000-20000$ | $16$ |
| $20000-25000$ | $3$ |
| $25000-30000$ | $3$ |
| $30000-35000$ | $2$ |
| $35000-40000$ | $1$ |
Calculate the modal income (in $Rs.$).
Medium
View SolutionThe maximum bowling speeds,in $km/h$,of $33$ players at a cricket coaching centre are given as follows:
Speed $(km/h)$ $85-100$ $100-115$ $115-130$ $130-145$ Number of players $11$ $9$ $8$ $5$
Calculate the median bowling speed (in $km/h$).
| Speed $(km/h)$ | $85-100$ | $100-115$ | $115-130$ | $130-145$ |
| Number of players | $11$ | $9$ | $8$ | $5$ |
Calculate the median bowling speed (in $km/h$).
Medium
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