Ex.14.4 Q1 Statistics Solution - NCERT Maths Class 9

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Question

The following number of goals were scored by a team in a series of \(10\) matches:

\(2, 3, 4, 5, 0, 1, 3, 3, 4, 3\)

Find the mean, median and mode of these scores.

Text Solution

 

What is known?

Number of goals was scored by a team in a series of \(10\) matches

What is unknown?

Mean, median and mode.

Reasoning:

 The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.

The median is that value of the given number of observations, which divides it into exactly two parts. So, when the data is arranged in ascending (or descending) order the median of ungrouped data can be calculated based on no. of observation are even or odd.

The mode is that value of the observation which occurs most frequently.

Steps:

The number of goals scored by the team is 

 \(2, 3, 4, 5, 0, 1, 3, 3, 4, 3\)

\[\begin{align}\,\,\overline{\rm{Mean}}\,{\rm{of }}\,{\rm{data}}\,&=\frac{\text { Sum of all the observations }}{\text { Total number of observations }}\\ \\ \overline\,{\rm{Mean}}\,{\rm{score}} &=\frac{2+3+4+5+0+1+3+3+4+3}{10}\\ \\ &=\frac{28}{10} \\ &=2.8 \\&= \,2.8\,\,{\rm{goals}}\end{align}\]

Arranging them in ascending order we get

\(0, 1, 2, 3, 3, 3, 3, 4, 4, 5\)

The number of observations is \(10\), which is an even number. Therefore, median score will be the mean of\(\frac{{10}}{2}\) i.e.,\( 5\) th \(\frac{{10}}{2}\) and \(+ 1\) i.e., \(6\) th observation while arranged in ascending or descending order.

\[\begin{align}{\text{Median}}\,{\text{score}}\,&= \frac{{{5^{th}}\,{\text{observation}}\,{\rm{ + }}\,{6^{{\rm{th}}}}{\text{observation}}\,}}{2}\\&= \frac{{3 + 3}}{2}\\ &= \frac{6}{2}\\ &= 3\end{align}\]

Mode of data is the observation with the maximum frequency in data.

Therefore, the mode score of data is \(3\) as it has the maximum frequency as \(4\) in the data.

  
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