Question

Two waiters at a cafe each served 10 large fruit smoothies. The amount in each large smoothie is shown below. Witch Waiter's smoothies showed less variability

Answer 1

Waiter’s B Large Smoothies showed less variability.

Explanation:

First, we have to find the mean for Waiter A’s and Waiter B’s Large Smoothies.

1) Mean

Waiter A

19.1 + 20.1 + 20.9 + 19.6 + 20.9 + 19.5 + 19.2 + 19.4 + 20.3 + 20.9 = 199.9

199.9 / 10 = 19.99

Waiter B

20.1 + 19.6 + 20.0 + 20.5 + 19.8 + 20.0 + 20.1 + 19.7 + 19.9 + 20.4 = 200.1

200.1 / 10 = 20.01

Now, we have to use the Mean Absolute Deviation (MAD) to find which waiter’s smoothies showed less variability.

Waiter A

I19.99 - 19.1I = 0.89

I19.99 - 20.1I = 0.11

I19.99 - 20.9I = 0.91

I19.99 - 19.6I = 0.39

I19.99 - 20.9I = 0.91

I19.99 - 19.5I = 0.49

I19.99 - 19.2I = 0.79

I19.99 - 19.4I = 0.59

I19.99 - 20.3I = 0.31

I19.99 - 20.9I = 0.91

0.89 + 0.11 + 0.91 + 0.39 + 0.91 + 0.49 + 0.79 + 0.59 + 0.31 + 0.91 = 6.3

6.3 / 10 = 0.63

Waiter B

I20.01 - 20.1I = 0.09

I20.01 - 19.6I = 0.41

I20.01 - 20.0I = 0.01

I20.01 - 20.5I = 0.49

I20.01 - 19.8I = 0.21

I20.01 - 20.0I = 0.01

I20.01 - 20.1I = 0.09

I20.01 - 19.7I = 0.4

I20.1 - 19.9I = 0.2

I20.1 - 20.4I = 0.3

0.09 + 0.41 + 0.01 + 0.49 + 0.21 + 0.01 + 0.09 + 0.4 + 0.2 + 0.3 = 2.2

2.2 / 10 = 0.22

Now, we just have to compare those numbers.

0.63 > 0.22

So, Waiter B’s smoothies show less variability.