Question

Use the data in Table 1 to perform the following tasks:

• Construct a cumulative frequency distribution (Ogive) using the speed class width (interval) of 5 mph
• Determine the pace, and
• Determine whether or not the mean speed exceeds the posted speed limit of 55 mph at 5% level of significance.

TABLE 1 Speed Data

Observed vehicular speed class (mph)	Observed frequency
35-39	1
40-44	2
45-49	2
50-54	10
55-59	5
60-64	5
65-69	3
70-74	3
75-79	2
80-84	2

Answer 1

Following table shows the data set for ogive

Lower limit	Upper limit	Lower boundary	Upper boundary	Freqeuncy, f	Cumualtive Frequency, cf
30	34	29.5	34.5	0	0
35	39	34.5	39.5	1	1
40	44	39.5	44.5	2	3
45	49	44.5	49.5	2	5
50	54	49.5	54.5	10	15
55	59	54.5	59.5	5	20
60	64	59.5	64.5	5	25
65	69	64.5	69.5	3	28
70	74	69.5	74.5	3	31
75	79	74.5	79.5	2	33
80	84	79.5	84.5	2	35

Now we need to plot upper boundary on x axis and cumulative freqeuncy of y axis. Following is the ogive:

It shows that there is a sudden hike at speed limit 49.5 .

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Now we need to find mean and SD of data set. Following table shows the calculations:

Class limits
Lower	Upper	Mid point, X=(lower+upper)/2	f	fx	f(X-mean)^2
35	39	37	1	37	484
40	44	42	2	84	578
45	49	47	2	94	288
50	54	52	10	520	490
55	59	57	5	285	20
60	64	62	5	310	45
65	69	67	3	201	192
70	74	72	3	216	507
75	79	77	2	154	648
80	84	82	2	164	1058
Total			35	2065	4310

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Conclusion:

There is evidence to conclude that the mean speed exceeds the posted speed limit of 55 mph at 5% level of significance.