Question

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.

Answer 1

Consider the data set:

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

Let arrange the given points scored in ascending order, we get:

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

Number of given observations in this data set is 16 that is even.

So, median will be calculated as follows:

Median = `((n/2)^(th)  "observation" + (n/2 + 1)^(th)  "observation")/2`

= `((16/2)^(th)  "observation" + (16/2 + 1)^(th)  "observation")/2`

= `((8)^(th)  "observation" + (9)^(th)  "observation")/2`

= `(10 + 14)/2`

= `24/2`

= 12

As we know that, mode is the observation which is repeated maximum number of times that is 10.

Hence, median and mode for the given data are 12 and 10, respectively.