Question

Find the median of the data 19, 25, 59, 48, 35, 31, 30, 32, 51. If 25 is replaced by 52, what will be the new median?

Answer 1

Finding the original median

arrange the given data in ascending order

19,25,30,31,32,35,48,51,59

number of observations = 9 (which is odd)

when n = odd the formula = $\frac{n + 1}{2}$

                                           =$\frac{9 + 1}{2}$

                                           = 5th term

so the 5th term = 32 is the original median

25 is replaced by 52

19,30,31,32,35,48,51,52,59

number of observations = 9 (which is odd)

when n = odd the formula = $\frac{n + 1}{2}$

                                           =$\frac{9 + 1}{2}$

                                           = 5th term

here the 5th term = 35 is the new median