We have a data set of 25 speeds clocked by radar.
a. We have to construct a grouped frequency distribution.
To start, we look at the range of the data set: the minimum value is 50 and the maximum value is 96, so we can construct 5 classes with a width of 10, starting at 50.
We then can construct the grouped frequency distribution as:
Speed Frequency
50 - 59 II (2)
60 - 69 IIIII I (6)
70 - 79 IIIII III (8)
80 - 89 IIIII I (6)
90 - 99 III (3)
We can construct a relative frequency distribution using the data from the previous distribution. The relative frequency of a class is the absolute frequency of that class divided by the size of the data set.
The relative frequency of each class will be:
Speed Relative frequency
50 - 59 2/25 = 0.08
60 - 69 6/25 = 0.24
70 - 79 8/25 = 0.32
80 - 89 6/25 = 0.24
90 - 99 3/25 = 0.12
We can graph this as:
We now have to convert this into an cumulative relative frequency, including percentile rank. We can do it as:
b. We have to graph an histogram of the data. This will be very similar to the graph of the relative frequency (the same shape), but the scale is different as we will use the absolute frequency:
c. The histogram shows that the distribution is bell shaped with no visible skewness.