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.
does the graph suggest that the distribution is skewed? if so, how?
a. the distribution appears to be skewed to the right (or positively skewed).
b. the distribution appears to be skewed to the left (or negatively skewed).
c. the distribution does not appear to be skewed.
d. the distribution appears to be skewed to both sides.
tornado f - scale frequency
0 24
1 16
2 2
3 3
4 1

Explanation:

Step1: Recall frequency - polygon construction

A frequency - polygon is constructed by plotting the mid - points of the class intervals on the x - axis and the frequencies on the y - axis and then connecting the points with straight lines. The mid - points for the given F - scale values \(0,1,2,3,4\) are considered.

Step2: Analyze the shape of the frequency polygon

To determine skewness from a frequency polygon, if the tail of the distribution extends to the right (higher values), it is right - skewed (positively skewed). If the tail extends to the left (lower values), it is left - skewed (negatively skewed).
Looking at the frequencies \(24,16,2,3,1\) for F - scale values \(0,1,2,3,4\) respectively, the frequencies are high for lower F - scale values and decrease as the F - scale value increases. This indicates that the tail of the distribution extends to the right.

Answer:

Construct a frequency polygon:
To construct the frequency polygon, we plot the points \((0,24)\), \((1,16)\), \((2,2)\), \((3,3)\), \((4,1)\) and connect them with straight lines. The correct graph is the one that matches these points.
For the skewness question:
A. The distribution appears to be skewed to the right (or positively skewed).