Answer to Question #243704 in Statistics and Probability for Jovy

Question

There are eight brothers and sisters in tala's family. Their ages are as follows: 22, 25, 14, 10, 7, 13 , 20, 6
Does the data show a symmetric distribution? explain

Answer 1

mean of the sample is 14.625

sample sort by ascending:6,7,10,13,14,20,22,25

Next step is to pair elements in the following way: (1)-(8), (2)-(7), (3)-(6), (4)-(5)

Now we will calculate the difference between mean and each element:

8.625 10.375 1 pair

7.625 7.375 2 pair

4.625 5.375 3 pair

1.625 -0.625 4 pair

Graphic result

As we can see, there is a much bigger difference between age and mean age in the second part of the sample(4 older kids), so there is no symmetry.