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 Solution$A$ company manufactures car batteries of a particular type. The lives (in years) of $40$ such batteries were recorded as follows:
$\begin{array}{llllllll}2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 \\ 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 \\ 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 \\ 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 \\ 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6\end{array}$
Construct a grouped frequency distribution table for this data,using class intervals of size $0.5$ starting from the interval $2 - 2.5$.
$\begin{array}{llllllll}2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 \\ 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 \\ 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 \\ 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 \\ 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6\end{array}$
Construct a grouped frequency distribution table for this data,using class intervals of size $0.5$ starting from the interval $2 - 2.5$.
Medium
View SolutionConsider the marks obtained (out of $100$ marks) by $30$ students of Class $IX$ of a school:
$\begin{array}{*{20}{c}}
{10}&{20}&{36}&{92}&{95}&{40}&{50}&{56}&{60}&{70} \\
{92}&{88}&{80}&{70}&{72}&{70}&{36}&{40}&{36}&{40} \\
{92}&{40}&{50}&{50}&{56}&{60}&{70}&{60}&{60}&{88}
\end{array}$
$\begin{array}{*{20}{c}}
{10}&{20}&{36}&{92}&{95}&{40}&{50}&{56}&{60}&{70} \\
{92}&{88}&{80}&{70}&{72}&{70}&{36}&{40}&{36}&{40} \\
{92}&{40}&{50}&{50}&{56}&{60}&{70}&{60}&{60}&{88}
\end{array}$
Medium
View SolutionIn a mathematics test given to $15$ students,the following marks (out of $100$) are recorded:
$41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60$
Find the mean,median,and mode of this data.
$41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60$
Find the mean,median,and mode of this data.
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
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