Question

A long straight road in a small town of New York is being used to monitor driving speeds.
The first 50 cars gave the results shown in Table 1 below. The figures are in km/h to
the nearest whole number.

45 60 71 57 67 78 90 81 78 91
65 88 67 66 50 68 67 73 63 94
48 90 79 95 65 70 75 61 54 67
57 59 85 84 70 81 40 59 76 59
77 78 97 75 72 77 54 68 67 74
Table 1

Answer the following questions:
(a) Find the range.

(b) Construct a frequency distribution for these data.

(c) Represent the data by a histogram and draw a frequency polygon on the
same graph. Hence, estimate the mode.

Answer 1

Answer on Question #63438 – Math – Statistics and Probability

Question

A long straight road in a small town of New York is being used to monitor driving speeds. The first 50 cars gave the results shown in Table 1 below. The figures are in km/h to the nearest whole number.

Table 1

Answer the following questions:

(a) Find the range.

(b) Construct a frequency distribution for these data.

(c) Represent the data by a histogram and draw a frequency polygon on the same graph. Hence, estimate the mode.

Solution

(a) The range.

$$R = X _ {\max } - X _ {\min }$$ $$X _ {\max } = 4 0$$ $$X _ {\min } = 9 7$$ $$R = 9 7 - 4 0 = 5 7$$

The range is 57.

(b) Frequency distribution

It is also possible to group the values. Here they are grouped in 3s:

The class width will be $57/3 = 19$ . Our classes will be 40-58, 59-77, and 78-97. Then, counting the number of entries in each class, we get

(c) Histogram and a frequency polygon:

The mode is 67 km/h.

Histogram and a frequency polygon for intervals:

The mode is 59-77 km/h.

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