Question

the given data represents a frequency distribution of the f - scale intensities of recent tornadoes. use the frequency distribution to construct a frequency polygon. does the graph suggest that the distribution is skewed? if so, how?
construct a frequency polygon using the data. choose the correct graph below.
tornado f - scale frequency
0 25
1 19
2 1
3 2
4 1

Explanation:

Step1: Determine class - midpoints

The classes are 0, 1, 2, 3, 4. The mid - points remain the same as the class values since they are single values.

Step2: Plot points

We plot the points \((0,25)\), \((1,19)\), \((2,1)\), \((3,2)\), \((4,1)\) and connect them with line segments. Also, we add two additional points at the mid - points of the classes just outside the range of our data (mid - point of class before 0 and mid - point of class after 4) with frequency 0. For the class before 0, we consider mid - point \(- 1\) with frequency 0 and for the class after 4, we consider mid - point 5 with frequency 0.

Step3: Analyze the shape

The majority of the data (25 + 19 = 44 out of 25+19 + 1+2+1=48) is concentrated on the left side (F - scale 0 and 1). The tail of the distribution extends to the right (higher F - scale values). So the distribution is right - skewed.

The correct frequency polygon is the one that has points plotted as described above. Looking at the general shape of the distribution with most of the data on the left and a tail to the right, we can determine the correct graph.

Answer:

The distribution is right - skewed. To answer the multiple - choice part about the frequency polygon, we need to visually check which graph has points \((-1,0)\), \((0,25)\), \((1,19)\), \((2,1)\), \((3,2)\), \((4,1)\), \((5,0)\) connected in order. Without seeing the actual graphs in detail, we can't definitively say which of A, B, C, D is correct, but the key is to match the plotted points and the right - skewed shape. If we assume we have visually inspected the graphs: If the graph that has the highest frequencies at F - scale 0 and 1 and then decreases with a long tail to the right is graph B, then the answer for the frequency polygon part is B.