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. a. Determine and interpret the quartiles of the length for all tornadoes. 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. Step 1: Understand the variables involved. Here, we focus on the "length" variable of tornadoes, which measures how long each tornado was. Quartiles divide the data into four equal parts, helping us understand the distribution of tornado lengths.
2. Step 2: To find the quartiles for all tornadoes, use a statistical software or tool like StatCrunch. Load the data set "Tornadoes_2017" and select the variable "length". Then, calculate the first quartile (Q1), the median (Q2), and the third quartile (Q3). These values represent the 25th, 50th, and 75th percentiles, respectively.
3. Step 3: Interpret the quartiles: Q1 tells you the length below which 25% of tornadoes fall, Q2 (median) is the middle value, and Q3 indicates the length below which 75% of tornadoes fall. This helps describe the spread and central tendency of tornado lengths.
4. Step 4: To determine the interquartile range (IQR) for tornado lengths in Kansas (KS), filter the data to include only tornadoes from KS. Then calculate IQR using the formula: \(\text{IQR} = Q3 - Q1\), where Q3 and Q1 are the third and first quartiles of tornado lengths in KS.
5. Step 5: Compare the IQRs of tornado lengths between Iowa (IA) and Kansas (KS) to assess dispersion. The state with the larger IQR has tornado lengths that are more spread out or dispersed. Explain this by noting that a larger IQR means greater variability in tornado lengths within that state.

Key Concepts

Quartiles

Quartiles divide a data set into four equal parts, helping to understand the distribution. The first quartile (Q1) is the 25th percentile, the median (Q2) is the 50th percentile, and the third quartile (Q3) is the 75th percentile. They summarize data spread and identify where most values lie.

Interquartile Range (IQR)

The interquartile range measures the spread of the middle 50% of data, calculated as Q3 minus Q1. It is a robust measure of variability that is less affected by outliers, useful for comparing dispersion between groups or states.

Data Filtering and Comparison

Filtering data by conditions (e.g., State=IA or KS) allows focused analysis on subsets. Comparing statistics like IQR across states helps determine which has more variability in tornado lengths, providing insights into differences in tornado behavior regionally.