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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The blood groups of $30$ students of Class $VIII$ are recorded as follows:
$A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,$
$A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.$
Represent this data in the form of a frequency distribution table. Which is the most common,and which is the rarest,blood group among these students?
$A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,$
$A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.$
Represent this data in the form of a frequency distribution table. Which is the most common,and which is the rarest,blood group among these students?
Medium
View SolutionConsider a small unit of a factory where there are $5$ employees: a supervisor and four labourers. The labourers draw a salary of $Rs. 5,000$ per month each,while the supervisor gets $Rs. 15,000$ per month. Calculate the mean,median,and mode of the salaries of this unit of the factory.
Medium
View SolutionThirty children were asked about the number of hours they watched $TV$ programmes in the previous week. The results were found as follows:
$\begin{array}{rrrrrrrrrr}1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 \\ 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 \\ 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12\end{array}$
$(i)$ Make a grouped frequency distribution table for this data,taking class width $5$ and one of the class intervals as $5-10$.
$(ii)$ How many children watched television for $15$ or more hours a week?
$\begin{array}{rrrrrrrrrr}1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 \\ 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 \\ 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12\end{array}$
$(i)$ Make a grouped frequency distribution table for this data,taking class width $5$ and one of the class intervals as $5-10$.
$(ii)$ How many children watched television for $15$ or more hours a week?
Medium
View SolutionIn a particular section of Class $IX,$ $40$ students were asked about the months of their birth and the following graph was prepared for the data so obtained:
Observe the bar graph given above and answer the following questions:
$(i)$ How many students were born in the month of November?
$(ii)$ In which month were the maximum number of students born?
Observe the bar graph given above and answer the following questions:
$(i)$ How many students were born in the month of November?
$(ii)$ In which month were the maximum number of students born?
Medium
View SolutionFind the mode of the following marks (out of $10$) obtained by $20$ students:
$4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9$
$4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9$
Medium
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