Liam works at a zoo. He was looking at some data showing the masses of their 555 African elephants. The mean mass of the elephants was 3{,}800\,{\text{kg}}3,800kg3, comma, 800, start text, k, g, end text, and the median mass was 3{,}600\,{\text{kg}}3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed 2{,}700\,{\text{kg}}2,700kg2, comma, 700, start text, k, g, end text.
Lola then got very sick and lost weight until her mass reached 1{,}800\,{\text{kg}}1,800kg1, comma, 800, start text, k, g, end text.
How will Lola's mass decreasing affect the mean and median?
Answers
Given : 5 African elephants
The mean mass of the elephants was 3800 kg
The median mass of the elephants was 3600 kg
The smallest elephant, named Lola, weighed 2700 kg
Lola then got very sick and lost weight until her mass reached 1800 kg
To Find : How will Lola's mass decreasing affect the mean and median?
Solution:
2700 , A , 3600 , B , C
as Median is 3600 and lowest is 2700
now 2700 becomes 1800
1800 , A , 3600 , B , C
so Median remains the same as 3600
No change in Median
The mean mass of the elephants was 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
Hence new total mass = 19000 - 2700 + 1800
= 181000 kg
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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