Question

Construct an ogive using six classes. 3) The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a checkpoint. The results are listed below.

19 31 42 50 35 40 37 49 59 41 20 36 36 43 35 46 75 23 43 64 27 48 34 38 70 38 52 53 48 33
Construct a frequency distribution, a relative frequency distribution, midpoint, boundary, and a cumulative frequency distribution using six classes.

Answer 1

To create an ogive for the speed data, we first calculate the frequency distribution, then the cumulative frequency and relative frequency distributions, as well as the midpoints and boundaries for each class. Finally, we plot the cumulative frequency against the class boundaries.

Step-by-step explanation:

To construct an ogive (cumulative frequency graph) using six classes for the data provided, first, we need to create a frequency distribution. We must determine the range of the data by subtracting the smallest value from the largest value.

Then, divide this range by the number of classes to find the class width (round up if necessary). Using this width, we can define class boundaries and then count how many data points fall within each class for the frequency distribution.

Next, we convert the frequencies to a cumulative frequency distribution by adding each class's frequency to the sum of the frequencies of all previous classes. The relative frequency distribution is found by dividing the frequency of each class by the total number of data points.

The midpoint of each class is the value halfway between the lower and upper boundaries of the class. Lastly, boundaries can be calculated by subtracting 0.5 from each lower class limit and adding 0.5 to each upper class limit.

These steps will generate a complete ogive.