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

Examination of core statistical measures used in data analysis.

Lily Green

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Statistical Analysis: Measures of Central Tendency, Variance, andCorrelationQuestion 1:a)The mean number of weekly complaints = (13+15+8+16+8)/5 = 12b)To find out the median we need to order the data. The ordered data is 8,8,13,15,16. Nowmedian is the middlemost value in the ordered dataset which is 13. Thus the median forthis data is 13.c)The mode is the most frequent observation in the data. Here we can observe that thenumber 8 occurred twice and rest of the values occurred once. Thus the mode for thisdataset is 8.Question2:a)The meanof the dataset is (40+55+62+43+50+60+65)/7 = 53.571. The ordered dataset is40, 43, 50, 55, 60, 62 and 65. Thus median is 55. No value occurred more than once sothere is no mode. Thus we can see that the measures of central tendency is around 54 forthis dataset.b)The lowest value is 40 which is farther apart from the mean/median than the highestvalue 65 indicating that the data might be negatively skewed alittle.Question3:The mean ofthe dataset = (6+8+7+10+3+5+9+8)/8 = 7Variance =∑𝑥2−𝑛∗௠𝑒𝑎𝑛2𝑛−1=62+82+72+102+32+52+92+82−8∗728−1=5.1429Standard deviation = Square root of variance =2.2678Question4:Here n = 5.

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