Millersville University of Pennsylvania

Write one script for each question to answer the following questions using python and without using import. 1. What is the mean house price in the dataset? 2. What is the median house price in the dataset? What does the difference between the mean and median tell you about the data? 3. Is there a meaningful difference between house prices in Seattle and houses elsewhere? Use a statistical argument. 4. What is the average price of a 1-bedroom house? 2-bedroom house? 3-bedroom house? 4-bedroom house? 5-bedroom house? Answer all of these questions with one script and one pass over the text file. Do more bedrooms increase home price? Use a statistical argument. 5. What is the average price per square foot of a house (living space) in the Seattle area? 6. Are houses built since 1980 more expensive than houses built before 1980? Less expensive? Neither? Use a statistical argument.

Acquire the file city_temperature.csv from Kaggle. The first thing you will notice is that it is very large! There’s a line of text for each of 321 cities in the world for each day of every year from Jan 1, 1995, to May 13, 2020 meaning the file has 2,906,328 lines. There are almost infinite number of questions we can ask about this kind of data, so we’ll be returning to this file in future labs, once we have more advanced tools and knowledge. For now, accomplish the following tasks without using import. 1. In Spyder, write a script that determines the mean daily temperature for each of the 321 cities in the file. For this script, each city should only have one output, so there should be a total of 321 lines of output. The recommended approach to this problem is to iterate over the file using a for loop and using the enumerate function to break the file down into lines. 2. Modify your script from part 2. Instead of outputting all 321 mean temperatures, only output the names and temperatures of the hottest and coldest cities on average.

Let σ = (1345) and τ = (234) be permutations. (a) Find the composition σ ◦ τ and express the answer as a product of disjoint cycles. (b) Find the order of σ ◦ τ.

Determine the number of all primitive 125th roots of unity without listing all of them.

(a) Find the order of 142 in Z8000. (b) Find all of the elements of order 8 in Z8000.

Let a be an element of order n in a group G. Prove that a^m =e if and only if n|m.