MATH 1280 wa2

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McGill University *

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1280

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Mathematics

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Jan 9, 2024

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docx

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MATH 1280-01 Written Assignment Unit 2 Hitesh Verma (Instructor) Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows:  Pairs of sneakers owned             X                      Frequency         1 2 2 5 3 8 4 12 5 12 6 0 7 1 1. Find the mean 2. Find the samples standard deviation, s .  3. Complete the Relative Frequency column and the Cumulative Relative Frequency Column.  4. Find the first quartile.  5. Find the median. 6. Find the third quartile.  7. What percent of the students owned at least five pairs?  8. Find the 40th percentile.  9. Find the 90th percentile.  Mean The mean, denoted by μ, represents the average value of all observations in the dataset. To calculate the mean, we sum up all the values of X and divide by the total number of observations: Mean (μ) = (ΣX)/n = (122 + 53 + 8 + 4 + 1 + 2 + 5 + 1 + 2 + 6 + 0 + 7 + 1)/40 = 3.78
Sample Standard Deviation The sample standard deviation, denoted by s, measures the variability or dispersion of the data around the mean. To calculate the sample standard deviation, we first calculate the squared deviations from the mean for each observation: (X - μ)^2 = (122 - 3.78)^2 + (53 - 3.78)^2 + ... + (7 - 3.78)^2 Then, we sum up these squared deviations and divide by n - 1: Variance (σ^2) = Σ(X - μ)^2 / (n - 1) Sample Standard Deviation (s) = √(Variance) Sample Standard Deviation (s) = √(10,624.72 / 39) = 1.29 Relative Frequency and Cumulative Relative Frequency Relative frequency is the proportion of observations that fall within a given category. Cumulative relative frequency is the proportion of observations that fall within a given category or any preceding categories. Pairs of sneakers owned Frequency Relative Frequency Cumulative Relative Frequency 1 2 0.050 0.050 2 5 0.125 0.175 3 8 0.200 0.375 4 12 0.300 0.675 5 12 0.300 0.975
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