Answer:
Standard Deviation is 18.57 .
Step-by-step explanation:
We are given the frequency distribution for the speed of a sample of automobiles traveling on an interstate highway;
Speed (mph) Frequency (f) X X*f X - [tex]Xbar[/tex] [tex](X-Xbar)^{2}[/tex]
50 - 54 4 52 208 52 - 65 = -13 169
55 - 59 3 57 171 57 - 65 = -8 64
60 - 64 2 62 124 62 - 65 = -3 9
65 - 69 5 67 335 67 - 65 = 2 4
70 - 74 2 72 144 72 - 65 = 7 49
75 - 79 5 77 385 77 - 65 = 12 144
∑f = 21 ∑X*f = 1367
Mean of the data, [tex]Xbar[/tex] = [tex]\frac{\sum Xf}{\sum f}[/tex]
= [tex]\frac{1367}{21}[/tex] = 65.09 ≈ 65 .
Now, Standard deviation, s = [tex]\sqrt{\frac{\sum f*(X-Xbar)^{2} }{n-1}}[/tex]
s = [tex]\sqrt{\frac{(4*169)+(3*64)+(2*9)+(5*4)+(2*49)+(5*144)}{6-1} }[/tex] = [tex]\sqrt{\frac{1724}{5} }[/tex] = 18.57
Therefore, standard deviation is 18.57 .
