Question

Please help I'm so confused and I really need to get this done

Answer 1

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