Threaded Problem: Tornado The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. b. Determine the interquartile range of the length of tornadoes in Iowa (IA). Hint: If you are using StatCrunch, enter “State=IA” in the Where: box of the Summary Stats dialogue window. Determine the interquartile range of the length of tornadoes in Kansas (KS). Which state has lengths of tornadoes that are more dispersed? Explain.

Verified step by step guidance

1. First, filter the data set to include only tornadoes from Iowa (IA). If using StatCrunch, enter "State=IA" in the Where: box of the Summary Stats dialogue window to isolate the relevant data.
2. Next, calculate the first quartile (Q1) and the third quartile (Q3) of the tornado lengths for Iowa. These quartiles represent the 25th and 75th percentiles of the data, respectively.
3. Compute the interquartile range (IQR) for Iowa by subtracting Q1 from Q3 using the formula: \(\text{IQR} = Q3 - Q1\).
4. Repeat the same process for Kansas (KS): filter the data to include only tornadoes from Kansas, then find Q1 and Q3 for tornado lengths, and calculate the IQR for Kansas.
5. Compare the IQR values for Iowa and Kansas. The state with the larger IQR has tornado lengths that are more dispersed, meaning there is a greater spread in the middle 50% of tornado lengths.

Key Concepts

Interquartile Range (IQR)

The interquartile range measures the spread of the middle 50% of a data set by subtracting the first quartile (Q1) from the third quartile (Q3). It is a robust measure of variability that is less affected by outliers than the range. In this problem, the IQR helps compare the dispersion of tornado lengths within each state.

Data Subsetting and Filtering

Data subsetting involves selecting a specific portion of a data set based on criteria, such as filtering tornado data by state (e.g., Iowa or Kansas). This allows focused analysis on relevant groups, ensuring that summary statistics like the IQR are calculated only for the tornadoes in the chosen state.

Comparing Variability Between Groups

Comparing variability involves analyzing measures like the IQR to determine which group has more spread or dispersion in data values. Here, comparing the IQRs of tornado lengths in Iowa and Kansas reveals which state experiences more variation in tornado lengths, aiding in understanding differences in tornado characteristics.