BIOL2060 W24 Problem Set 2 (1)

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York University *

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Biology

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Apr 3, 2024

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NOT FOR SALE OR DISTRIBUTION – PROPERTY OF YORK UNIVERSITY BIOL 2060 – Winter 2024 Tutorial Problem Set #2. Total marks = 31 Work in a group of three on this problem set, using the laptop of one person in the group. You will need: 1) Excel and 2) R and RStudio. You can use the desktop version on your laptop (recommended) or access it online via myapps.yorku.ca. At the end of the tutorial each group will submit by email to your TA answers to the questions in a 1) Word document with answers to the questions, 2) an Excel file showing all formulas and calculations, 3) an R script showing all code used, and 4) a handwritten work for all calculations done by hand. In the body of the email, list the names and student numbers of the three members of your group. Submit your work to your TA at the end of the session, using the email they will provide. 1. For the data sets below, use Excel to determine each of the following. Note that during your tests and the exam you will be required to do these calculations by hand, i.e., using a calculator and showing your work. For practice (after the tutorial) consider doing these same calculations by hand and checking your answers. [6 marks] a) Sample size, n b) Sum the values, ∑ Y 𝑛 𝑖=1 𝑖 c) Square of the sum of values ( ∑ 𝑌𝑖 𝑛 𝑖=1 ) 2 d) Sum of squared values, ∑ 𝑌𝑖 𝑛 𝑖=1 2 e) Sum of squared deviations from the mean (SS), ∑ (𝑌 𝑖 𝑛 𝑖=1 - 𝑌 ̅ ) 2 f) Median g) Mean h) Variance i) Standard deviation j) Coefficient of variation Data Set 1 Data Set 2 Data Set 3 13.3 0 152.5 24.6 -15 -10.2 18.5 2 31.6 11.3 14 81.4 22.9 -2 -92.1

2. Use R to estimate all the quantities in Q1 above for the three data sets. You may need to do a bit of research or be creative in your approach to some of the calculations. [6 marks] 3. With the rise of online education, students are spending varying amounts of time (minutes) on virtual learning platforms. The time spent on virtual learning per week by two groups of students (Group P and Group Q) is recorded as follows. Estimate the median, 1st quartile, 3rd quartile, and interquartile range for each group. Do this by hand (with a calculator as necessary) and show your work. [4 marks]. Data for Group P: {100,135,40,90,115,175,230, 185,160,95, 200} Data for Group Q: {110,125,90,210, 280, 150,60,170,185,255, 130} 4. Use Excel to calculate the quantities in Q3 above for each of the two datasets. [2 marks] 5. Use R to calculate the quantities in Q3 above for each of the two datasets. [4 marks] 6. Data manipulation using Excel allows you to update, modify, delete, and input data into a database. This gives the user a better understanding of the data set and to obtain in-depth insights. Using Excel, explore the effects of the following transformations using the data from time groups in Q3 above. Calculate the mean and standard deviation on the raw data for both Time groups. Then perform the transformations below on each data set. Re-calculate the mean and standard deviations on the transformed data. Type a sentence on the Excel sheet noting how the mean and standard deviation are affected by each transformation. a) add 30 to each data point (30 minutes added to the time of each student) b) take the square root of each data point c) take the log base 10 of each number [6 marks] 7. You are conducting a study on the monthly expenses of urban households in a metropolitan city. You collect the following data representing the monthly spending (in dollars) of a random sample of households: $2,500, $3,000, $12,000, $3,500, $4,200 Estimate both the mean and median monthly expenses of urban households using your preferred approach. Which statistic would you consider to be the better indicator of monthly expenses and why? [3 marks]

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