8 655 684 718 741 770 848 856 864 864 720 a What happens to

8

655

684

718

741

770

848

856

864

$864

$720

(a) What happens to the median?

It decreases by

$

It increases by

$

It stays the same

(b) What happens to the mean?

It decreases by

$

It increases by

$

It stays the same

Solution

a) Median:

Data is ascending order: 655, 684, 718, 741, 770, 848, 856, 864

Initial median: n = 8 which is even so it has 2 middle terms i.e. (n/2) and (n/2 + 1)

Median = (4th + 5th term)/2 = (741+ 770)/2 = 1511/2 = 755.5

After change in value, data in ascending order: 655, 684, 718, 720, 741, 770, 848, 856

n = 8 which is even so it has 2 middle terms i.e. (n/2) and (n/2 + 1)

Median = (4th + 5th term)/2 = (720 + 741)/2 = 1461/2 = 730.5

So, median reduces from 755.5 to 730.5 = 25

b) Initial Mean = Sum of Observations / Total number of observations = (655 + 684 + 718 + 741 + 770 + 848 + 856 + 864)/8 = 6136/8 = 767

New mean = (655 + 684 + 718 + 720 + 741 + 770 + 848 + 856)/8 = 749

So, mean decreases from 767 to 749 = 18