Question

The speeds of 183 cars in a race are shown in the table below. Find the th 5.5-615.5 722.34 763.46

Answer 1

Speed	freq	cumulative freq.
475.5 - 545.5	26	26
545.5-615.5	16	42
615.5-685.5	44	86
685.5-755.5	19	105 <--
755.5-825.5	25	130
825.5-895.5	22	152
895.5-965.5	31	183

kth percentile is given by :

100

• L is the lower limit of the class containing P_k
• f is the frequency of the class containing P_k
• h is the width of the class containing P_k
• C is the cumulative frequency of the class preceding the class containing P_k

Note that k = 52 , N= 183 , So KN/100 = 95.16

This freq lies in the class 685.5 - 755.5

So, L =685.5

f = 19

h = 70

c= 86

So,  

95.16-86_ × 70 = 719.24 Po = 685.5 19

b)

class limit	class boundary	freq,
30-39	29.5-39.5	3
40-49	39.5-49.5	16
50-59	49.5-59.5	50
60-69	59.5-69.5	16
70-79	69.5-79.5	22

Class width of a class = Upper boundary - lower boundary of that class

So, classwidth = 10

Mid point of 3rd class = (59.5+49.5)/2 = 54.5

c)

Ho: μ-25) against μ 25