Give one example of a situation in which $(i)$ the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
(N/A) When a data set contains a few observations that are significantly distant from the rest of the data (outliers),the mean is heavily influenced by these extreme values,making it an inappropriate measure of central tendency. In such cases,the median is a more robust and appropriate measure.
Consider the following data representing the marks obtained by $12$ students in a test:
$48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99$
In this data set,the values $97$ and $99$ are significantly higher than the other marks. Because of these extreme values,the mean would be skewed upwards,failing to represent the typical performance of the students. Therefore,the median is a more appropriate measure of central tendency for this data.
Consider the following data representing the marks obtained by $12$ students in a test:
$48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99$
In this data set,the values $97$ and $99$ are significantly higher than the other marks. Because of these extreme values,the mean would be skewed upwards,failing to represent the typical performance of the students. Therefore,the median is a more appropriate measure of central tendency for this data.
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Similar Questions
The points scored by a Kabaddi team in a series of matches are as follows:
$17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28$
Find the median of the points scored by the team.
$17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28$
Find the median of the points scored by the team.
Medium
View SolutionThree coins were tossed $30$ times simultaneously. Each time the number of heads occurring was noted down as follows:
$\begin{array}{llllllllll}0 & 1 & 2 & 2 & 1 & 2 & 3 & 1 & 3 & 0 \\ 1 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 \\ 3 & 0 & 0 & 1 & 1 & 2 & 3 & 2 & 2 & 0\end{array}$
Prepare a frequency distribution table for the data given above.
$\begin{array}{llllllllll}0 & 1 & 2 & 2 & 1 & 2 & 3 & 1 & 3 & 0 \\ 1 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 \\ 3 & 0 & 0 & 1 & 1 & 2 & 3 & 2 & 2 & 0\end{array}$
Prepare a frequency distribution table for the data given above.
Easy
View SolutionLet us consider the following frequency distribution table which gives the weights of $38$ students of a class:
Weights (in $kg$) Number of students $31-35$ $9$ $36-40$ $5$ $41-45$ $14$ $46-50$ $3$ $51-55$ $1$ $56-60$ $2$ $61-65$ $2$ $66-70$ $1$ $71-75$ $1$ Total $38$
If two new students of weights $35.5\, kg$ and $40.5\, kg$ are admitted to this class,how should the frequency distribution table be adjusted to include them?
| Weights (in $kg$) | Number of students |
| $31-35$ | $9$ |
| $36-40$ | $5$ |
| $41-45$ | $14$ |
| $46-50$ | $3$ |
| $51-55$ | $1$ |
| $56-60$ | $2$ |
| $61-65$ | $2$ |
| $66-70$ | $1$ |
| $71-75$ | $1$ |
| Total | $38$ |
If two new students of weights $35.5\, kg$ and $40.5\, kg$ are admitted to this class,how should the frequency distribution table be adjusted to include them?
Difficult
View SolutionThe following table gives the life times of $400$ neon lamps:
The time (in hours) Number of lamps $300-400$ $14$ $400-500$ $56$ $500-600$ $60$ $600-700$ $86$ $700-800$ $74$ $800-900$ $62$ $900-1000$ $48$
$(i)$ Represent the given information with the help of a histogram.
$(ii)$ How many lamps have a life time of more than $700$ hours?
| The time (in hours) | Number of lamps |
| $300-400$ | $14$ |
| $400-500$ | $56$ |
| $500-600$ | $60$ |
| $600-700$ | $86$ |
| $700-800$ | $74$ |
| $800-900$ | $62$ |
| $900-1000$ | $48$ |
$(i)$ Represent the given information with the help of a histogram.
$(ii)$ How many lamps have a life time of more than $700$ hours?
Medium
View SolutionFind the mode of $14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.$
Easy
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