A) Five-number summary:
1. sample minimum
2. first quartile
3. median
4. third quartile
5. maximum
0) Order the data
State A: 4, 5, 6, 6, 7, 8, 9, 21, 25
State B: 10, 11, 12, 13, 14, 14, 15, 15, 16
1) Minimum:
State A: 4
State B: 10
2) Median: the middle of the sample
State A: 7
State B: 14
3) first quartle : the median of the first half:
State A: (5+6)/2 = 5.5
State B: (11+12)/2 = 11.5
4) third quartile: the median of the higher half
State A: (9+21) /2 = 15
State B: 15
5) Sample maximum:
State A: 25
State B: 16
6) Interquartile range: 3rd quartile - 1st quartile
State A: 15 - 5.5 = 9.5
State B: 15 - 11.5 = 4.5
B) Symmetry:
Distance to the median and the quartiles:
State A:
median - first quartile: 7 - 5.5 = 1.5
third quartile - median: 15 - 7 = 8
1.5 ≠ 8 => skewed (not symmetrical)
State B
median - first quartle : 14 - 11.5 = 2.5
third quartile - median: 15 -14 = 1
2.5 ≠ 1 => skewed