Respuesta :
Answer:
(a) Mean = 60.684
(b) Variance = 31.2292 Standard deviation = 5.5883
Step-by-step explanation:
We are given the following frequency distribution of speeds;
Speed (miles per hour) Frequency (f) X X * f
45-49 10 47 470
50-54 40 52 2080
55-59 150 57 8550
60-64 175 62 10850
65-69 75 67 5025
70-74 15 72 1080
75-79 10 77 770
[tex]\sum f[/tex] = 475 [tex]\sum Xf[/tex] = 28825
(a) Mean speed of the automobiles, [tex]Xbar[/tex] = [tex]\frac{\sum Xf}{\sum f}[/tex] = [tex]\frac{28825}{475}[/tex] = 60.684
(b) Variance formula is given by = [tex]\frac{\sum (X_i - Xbar)^{2} * f }{\sum f - 1}[/tex]
This mean variance is given by subtracting each X value from the mean and then squaring each value and then multiplying it with the corresponding frequency.
Variance = [tex]\frac{(47 - 60.684)^{2} * 10 + (52 - 60.684)^{2} * 40 + ......... + (77 - 60.684)^{2} * 10}{475 -1}[/tex]
= 31.2292
Standard Deviation = [tex]\sqrt{ Variance}[/tex] = [tex]\sqrt{ 31.2292}[/tex] = 5.5883 .
