University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

128

Pages:

2
Author:

Niklas

Given Sample: 30, 35, 35, 34, 32, 31 Parts: a) Compute the mean, the median, and the mode. b) Suppose to add another measurement to the sample and the mean increases to 70. What is the value of the added measurement? c) Compute the variance. d) Compute the interquartile range. e) Use a boxplot to represent the data. Solutions: a) Mean, Median, and Mode Mean: (30 + 35 + 35 + 34 + 32 + 31) / 7 = 33.5 Median: (34 + 35) / 2 = 34.5 Mode: 35 b) Added Measurement 70 = (245 + x) / 8 x = 560 - 245 = 315 c) Variance Variance = Σ(ni * (xi - x̄)²) / N = 68660 / 8 = 8582.5 d) Interquartile Range (IQR) Q1 = P25 = 33 Q3 = P75 = 39 IQR = Q3 - Q1 = 39 - 33 = 6 e) Boxplot Lower whisker: Q1 - 1.5 * IQR = 33 - 1.5 * 6 = 24 Upper whisker: Q3 + 1.5 * IQR = 39 + 1.5 * 6 = 48 Exercise 2 In a sample of 12 scores, the largest score is increased by 36 points. What effect will this have on the mean of the scores? Solution: We don't have the value of the different data, so we don't know which one of the data is the largest but it is not really relevant. Let: a, b, c, d, e, f, g, h, i, l, m, n be the individual scores Before the increase: Mean = (a + b + c + d + e + f + g + h + i + l + m + n) / 12 Now we add the 36 points: New mean = (a + b + c + d + e + f + g + h + i + l + m + n + 36) / 12 Simplifying: New mean = (a + b + c + d + e + f + g + h + i + l + m + n) / 12 + 36 / 12 New mean = Old mean + 3