Math Problem Statement

The data in the accompanying table represent a variety of variables measured on a random sample of 100 100 tornadoes that occurred between 1950 and 2020. Complete parts​ (a) through​ (c). LOADING... Click the icon to view the tornado data. State F Scale PropLoss Length SD 1 3 0.1 IN 1 1 17.5 KY 1 20000 0.79 NE 1 5 0.8 PA 0 6 5.6 TX 2 2 0.2 MI 1 0.003 0.09 WI 1 0 0.1 OK 0 0 2 CO 1 0 0.1 MN 2 0.002 2.5 OK 2 5 9.9 AR 0 5 5.7 LA 1 500000 3.93 OK 0 5 20 WI 1 6 5 FL 0 5 0.3 MN 0 4 8.4 IA 0 5 0.1 SD 0 0 3.25 FL 0 0 0.1 NC 2 0 0.12 AR 0 0.025 1 IN 0 0 8.5 MO 0 0 1 TX 2 0 0.2 CO 2 0 0.11 GA 0 250000 3.68 TX 0 4 2 TX 1 3 12.1 OH 2 0.016 0.97 NE 0 0 0.1 IA 0 6 4.3 IA 0 3 0.2 OK 0 0 1.4 TX -9 0 0.1 TX 0 2 1.5 KS 1 0 2 OK 0 3 0.5 TX 1 0 0.1 OK 1 4 1 WI 2 0 5.33 NJ 0 0.025 0.16 TX 1 0 0.1 TX 0 4 4.9 MO -9 5 2 AL 1 4 6.8 IL 1 0 0.1 CO 0 2 1 AR 1 0 4 KS -9 0 0.62 MN 0 2 1.5 OK 0 0 0.1 OK 1 0 22.2 TX 1 0 2 MO 0 5 5 OK 1 5 10 MI 2 6 19 MT 1 0 0.1 AR 0 0 3 OH -9 0 0.1 SC 1 0 6.01 MO 1 2 0.3 MI 2 0 2.5 CO 2 0 1 TX 1 4 0.1 NC 2 0.2 0.2 KY 0 0 0.28 IA 0 4 0.1 TX 1 0 0.58 SC 0 0 0.5 MI 0 1 0.2 IL 1 0 0.1 NY 0 4 17 WI 1 75000 3.51 KS 0 0.05 3.3 WI 0 0 0.1 GA 1 5 1.5 OK 0 0 0.1 OH 0 5 2 MO 0 750000 0.95 KS 0 0 0.1 AR 1 0.025 3.13 TX 0 4 0.2 KS 0 0 0.2 AR 1 4 14.9 MO 0 0.13 3.9 KS 0 0 0.3 KY 1 0.25 8.4 AL 1 0.3 8.2 LA 1 0.03 1 SD 1 0.5 0.6 TN -9 4 21 TX 1 0 0.02 KS 1 0.025 2.07 WI 1 4 0.1 MS 2 3 2 VA 1 5 0.2 IN 2 0 1.25 TX 2 0 0.1 ​(a) Determine the mean and median length of the tornadoes. The mean length is x overbar x equals

3.23 3.23 ​mile(s). ​(Round to two decimal places as​ needed.) Part 2 The median length is M equals

1 1 ​mile(s). ​(Type an integer or a decimal. Do not​ round.) Part 3 Based on the values of the mean and​ median, what shape would one expect a histogram of tornado length to​ have? (Consider the mean and median to be meaningfully different if they are more than 0.05​ apart.) One would expect the histogram to be skewed right. Part 4 ​(b) Determine the mean and median property loss for all tornadoes. The mean property loss is x overbar x equals =​$ 15,951.61 15,951.61. ​(Round to two decimal places as​ needed.) Part 5 The median property loss is M equals =​………….. $ enter your response here . ​(Type an integer or a decimal. Do not​ round.)

Solution

To calculate the median property loss, we first need to arrange the property loss values (PropLoss) in ascending order and find the middle value.

The property loss values (PropLoss) from the data provided are as follows:

  • 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.002, 0.003, 0.005, 0.016, 0.025, 0.025, 0.025, 0.03, 0.05, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.11, 0.12, 0.2, 0.2, 0.2, 0.25, 0.3, 0.3, 0.5, 1, 1.5, 1.5, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6.01, 75000, 20000, 250000, 500000, 750000

Since there are 100 values, the median will be the average of the 50th and 51st values.

Now, let's locate the 50th and 51st values in the sorted list:

  • The 50th value is 4, and the 51st value is also 4.

Thus, the median property loss is:

Median Property Loss=4+42=4\text{Median Property Loss} = \frac{4 + 4}{2} = 4

Therefore, the median property loss is $4.

Would you like any further details, or do you have any questions?

Here are 5 related questions you can explore:

  1. How would you calculate the mode of property loss in this dataset?
  2. What is the range of the property loss values?
  3. How would outliers in property loss affect the mean and median?
  4. How does the skewness of property loss compare to tornado length?
  5. How can you create a histogram of tornado property loss using this data?

Tip: When the mean is higher than the median, it typically suggests a right-skewed distribution.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Mean
Median
Distribution Shape
Skewness

Formulas

Mean formula: Mean = Σx / n
Median calculation: Middle value of an ordered dataset
Right-skewed distribution: Mean > Median

Theorems

Skewness in Distributions

Suitable Grade Level

Grades 10-12

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