graph 1 (18, 20, 20, 20, 21, 22, 22)

Question

graph 2 (0, 2, 2, 2, 2, 4, 4, 4, 5, 5)
which of the two graphs has a larger standard deviation

Answer 1

To determine which of the two graphs has a larger standard deviation, calculate the standard deviation for each set of numbers.

For graph 1:
Mean = (18+20+20+20+21+22+22) / 7 = 143 / 7 = 20.43
Calculate the variance:
((18-20.43)^2 + (20-20.43)^2 + (20-20.43)^2 + (20-20.43)^2 + (21-20.43)^2 + (22-20.43)^2 + (22-20.43)^2) / 7 = 1.7757
Standard deviation = sqrt(1.7757) = 1.33

For graph 2:
Mean = (0+2+2+2+2+4+4+4+5+5) / 10 = 26 / 10 = 2.6
Calculate the variance:
((0-2.6)^2 + (2-2.6)^2 + (2-2.6)^2 + (2-2.6)^2 + (2-2.6)^2 + (4-2.6)^2 + (4-2.6)^2 + (4-2.6)^2 + (5-2.6)^2 + (5-2.6)^2) / 10 = 2.04
Standard deviation = sqrt(2.04) = 1.43

Therefore, the first graph has a larger standard deviation than the second graph.