1. Report the mean, median, and mode for the following data set of worm lengths measured in centimeters: 6, 4, 11, 12, 13, 9, 10, 14, 8, 4, 7, 12 Please include extras such as the standard deviation, sample size, range, etc. 2. Mr. Jones gave an exam to his environmental science class. The students earned the following grades: 45, 50, 55, 55, 60, 60, 65, 65, 65, 65, 65, 75, 75, 80, 85, 85, 85, 85, 85, 85, 90, 90, 95,100. Mr. Jones graphed the class's scores. Fig. 5.1 Grade Distribution for Environmental Science Exam #1 7 6 5 4 Number of Students 3 2 1 0 40 50 60 70 80 90 100 110 120 Grade (%) What is the best measure of central tendency for Mr. Jones's grade distribution? How should Mr. Jones report it? For this question, the graph is key. Notice there are two distinct peaks which means that many students had those same two grades Is there a better measure of central tendency when conveying the most common values? 3. A real estate agent has been given 10 houses to list. The house prices in dollars are: 110,000, 95,000, 87,000, 92,000, 99,000, 250,000, 265,000, 210,000, 275,000, 240,000 Please include extras such as the standard deviation, sample size, range, etc. 4. Matthew collected the following data: Table 4.1 Effect of Diazinon Exposure on Tadpole Length Tadpole length (cm) Control 0.25 ppb 0.5 ppb Tadpole 1 4.4 4.4 3.1 Tadpole 2 4.6 3.5 3.4 Tadpole 3 4.2 3.8 3.7 Tadpole 4 3.8 4.2 4.0 Tadpole 5 4.3 4.1 3.3 Mean (cm) 4.26 4.0 3.5 Std Dev (cm) 0.3 0.4 0.4 t-test probability NA 0.122 0.003 (p-value) 1.0 ppb 3.5 3.1 2.8 3.3 2.6 3.06 0.4 0.0002 Based on the data presented in the table above, are any of the treatment groups significantly different from the control group? If so, which groups are different and how do you know they are different? 5. Natalie conducted a study on the effects of triclosan on three algae populations. She collected an algae sample from three different ponds, counted the number of algae cells present in the sample, and then exposed them to a 5-ppm aqueous solution of triclosan and re-counted the number of algae cells in each sample. Using a paired t-test, she obtained a p-value of 0.083 when comparing the original algae population sizes to the population sizes after exposure to triclosan. Natalie concluded that triclosan is toxic to algae because her data for the three samples showed a trend toward a reduction in population size. What could Natalie do to show a statistically significant effect of triclosan on algae population size? For this question, the research did a statistical test and did not see a difference between the groups but the data was trending towards a difference