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  • The points scored by a basket ball team in a series of matches are as follows: 17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28 Find the median and mode for the data.

The points scored by a basketball team in a series of matches are as follows:

17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28

Find the median and mode for the data.

Answers (2)

Answer : [median = 12 and mode = 10]

Solution. To calculate the median, arrange the given data in ascending order and then find the middle term. This middle term is called the median.

Here total elements, n = 16 (even)

The terms as arranged in ascending order:

2, 5, 7, 7, 8, 10, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48

Number of observation = 16 (even number)

Now using the formula of the median in case number of terms is even

\Rightarrow \text{Median}=\frac{\left ( \frac{n}{2} \right )^{th}\text {obs}+\left ( \frac{n}{2}+1 \right )^{th}\text {obs}}{2}

=\frac{\left ( \frac{16}{2} \right )^{th}\text {obs}+\left ( \frac{16}{2}+1 \right )^{th}\text {obs}}{2}

  median=\frac{\left ( 8^{th}\text {obs.}+9^{th}obs. \right )}{2}

\Rightarrow \frac{10+14}{2}=\frac{24}{2}

Median =12

The mode is the value that occurs the most number of times in a given set of values

Now mode is 10 because it is the most repeating number.

Hence, median = 12 and mode = 10.

Posted by

infoexpert23

View full answer

Answer : [median = 12 and mode = 10]

Solution. To calculate the median, arrange the given data in ascending order and then find the middle term. This middle term is called the median.

Here total elements, n = 16 (even)

The terms as arranged in ascending order:

2, 5, 7, 7, 8, 10, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48

Number of observation = 16 (even number)

Now using formula of median in case number of terms is even

\Rightarrow Median =\frac{\left ( \frac{n}{2} \right )^{th}\text {obs}+\left ( \frac{n}{2}+1 \right )^{th}\text {obs}}{2}

=\frac{\left ( \frac{16}{2} \right )^{th}\text {obs}+\left ( \frac{16}{2}+1 \right )^{th}\text {obs}}{2}

So median =\frac{\left ( 8^{th}\text {obs.}+9^{th}obs. \right )}{2}

\Rightarrow \frac{10+14}{2}=\frac{24}{2}

Median =12

Mode is the value that occurs the most number of times in a given set of values

Now mode is 10 because it is the most repeating number.

Hence, median = 12 and mode = 10.

Posted by

infoexpert23

View full answer

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