Answer:
The correct options are;
City A tends to be warmer than City B
City A has more variable temperatures than city B
Step-by-step explanation:
For City A
The number line is from 20 to 70
The whiskers range = 30 to 63
The box range = Interquartile range = 50 to 60
Therefore;
Q₁ = 50
Q₃ = 60
The median = Q₂ = 55
For City B
The number line is from 20 to 70
The whiskers range = 40 to 70
The box range = Interquartile range = 43 to 55
Therefore;
Q₁ = 43
Q₃ = 55
The median = Q₂ = 53
Therefore;
The range of a box plot for City A is 63 - 30 = 33
The range of a box plot for City B is 70 - 40 = 30
The interquartile range for City A = 60 - 10 = 10
The interquartile range for City B = 55 - 43 = 12
The minimum temperature for City A = 30
The maximum temperature for City A = 63
The minimum temperature for City B = 40
The maximum temperature for City B = 70
Comparing the averages of the temperatures of each quartile, we have;
For City A
Total average temperature, T₁
T₁ = 0.25*40*30 + 0.25*52.5*30+0.25*57.5*30+0.25*61.5*30 = 1586.25
For City B
Total average temperature, T₂
T₂ = 0.25*41.5*30 + 0.25*48*30+0.25*54*30+0.25*62.5*30 = 1545
Hence, T₁ > T₂
Therefore, City A tends to be warmer than City B
Also
City A has more variable temperatures than city B as the range is larger and 25% of City B are between 40 and 43 and another 25% is between the temperatures of 53 and 55 and also 75% of City B are between 40 and 55 while 75% of City A are between 60 and 30.
