Question

A cat gave birth to 3333 kittens who each had a different mass between 147147147147 and 159 g159\,\text{g}159g159, start text, g, end text. Then, the cat gave birth to a 4th4^{\text{th}}4th4, start superscript, start text, t, h, end text, end superscript kitten with a mass of 57 g57\,\text{g}57g57, start text, g, end text. [Show data] How will the birth of the 4th4^{\text{th}}4th4, start superscript, start text, t, h, end text, end superscript kitten affect the mean and median? Choose 1 answer: Choose 1 answer: (Choice A) A Both the mean and median will decrease, but the median will decrease by more than the mean. (Choice B) B Both the mean and median will decrease, but the mean will decrease by more than the median. (Choice C) C Both the mean and median will increase, but the median will increase by more than the mean. (Choice D) D Both the mean and median will increase, but the mean will increase by more than the median.

Answer 1

Answer:

The correct option is (B).

Step-by-step explanation:

The median (m) is a measure of central tendency. To obtain the median, we assemble the data in arising order. If the data is odd, the median is the mid-value. If the data is even, the median is the arithmetic-mean of the two mid-values.

The mean of a data set is:

$\bar X=\frac{1}{n}\sum\limits^{n}_{x=0}{X}$

For the three kittens it is provided that the weights are in the range 147 g to 159 g.

So, the mean and median weight for the 3 kittens lies in the middle of this range.

Now a fourth kitten is born, with weight 57 g.

Now the range of the weight of 4 kittens is, 57 g to 159 g.

The mean is going to decrease as one more value is added to the data and the value is the least.

The median will also decrease because now the median will be mean of the 2nd and 3rd values.

But the mean would decrease more than the median because a smaller value is added to the data.

Thus, the correct option is (B).