Statistical Analysis: Measures of Central Tendency, Variance, and Correlation

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Statistical Analysis: Measures of Central Tendency, Variance, and Correlation Question 1: a) The mean number of weekly complaints = (13+15+8+16+8)/5 = 12 b) To find out the median we need to order the data. The ordered data is 8,8,13,15,16. Now median is the middlemost value in the ordered dataset which is 13. Thus the median for this data is 13. c) The mode is the most frequent observation in the data. Here we can observe that the number 8 occurred twice and rest of the values occurred once. Thus the mode for this dataset is 8. Question 2 : a) The mean of the dataset is (40+55+62+43+50+60+65)/7 = 53.571. The ordered dataset is 40, 43, 50, 55, 60, 62 and 65. Thus median is 55. No value occurred more than once so there is no mode. Thus we can see that the measures of central tendency is around 54 for this dataset. b) The lowest value is 40 which is farther apart from the mean/median than the highest value 65 indicating that the data might be negatively skewed a l ittle. Question 3 : The mean of the dataset = ( 6 + 8 + 7 + 10 + 3 + 5 + 9 + 8 )/8 = 7 Variance = ∑ 𝑥 2 − 𝑛 ∗ ௠𝑒𝑎 𝑛 2 𝑛 − 1 = 6 2 + 8 2 + 7 2 + 10 2 + 3 2 + 5 2 + 9 2 + 8 2 − 8 ∗ 7 2 8 − 1 = 5.1429 Standard deviation = Square root of variance = 2.2678 Question 4 : Here n = 5.
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