Question

In the census population density dataset, what are the first, second and third quartiles?

1,19,35,43,49,55,56,56,63,67,94,105,110,168,175,181,212,231,239,351,461,595,738,839,9857

Answer 1

Solution:- GIven that values : 1,19,35,43,49,55,56,56,63,67,94,105,110,168,175,181,212,231,239,351,461,595,738,839,9857

The first quartiles : 55.5

Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

1 19 35 43 49 55 56 56 63 67 94 105 110 168 175 181 212 231 239 351 461 595 738 839 9857

So, the bottom half is

1 19 35 43 49 55 56 56 63 67 94 105

The median of these numbers is 55.5

The Second quartiles : 110

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

1   19   35   43   49   55   56   56   63   67   94   105   110   168   175   181   212   231   239   351   461   595   738   839   9857   

So, the median is 110 .

The third quartiles : 295

Explanation

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

1   19   35   43   49   55   56   56   63   67   94   105   110   168   175   181   212   231   239   351   461   595   738   839   9857   

So, the upper half is

168   175   181   212   231   239   351   461   595   738   839   9857   

The median of these numbers is 295