Question

2. The following data set represents the number of new computer accounts registered during ten consecutive days: 43,37, 50, 51, 58, 105, 52, 45, 45,10. a) Computer the mean, quartiles and standard deviation; b) Check for outliers using 1.5(IQR) rule c) Delete the detected outliers and compute the mean, quartiles and standara deviation; d) Explain the difference between results in a) and c)

Answer 1

Answer:

Following table shows the calculations for mean and standard deviaton (x-mean)42 (x-mean) 43.56 43 -6.6 158.76 12.6 37 0.16 0.4 50 1.96 51 70.56 8.4 58 3069.16 55.4 105 5.76 52 21.16 4.6 45 21.16 4.6 45 1568.16 -39.6 10 4960.4 496 Total Mean 2x 496 =-= 49.6 10 Standard deviation Σ (x-x)--23.477

Following is the ordered data set: 10 37 43 45 45 50 51 52 58 105 Median: Average of 5th and 6th data value: 45 +50 Median =- = 47.5 First Quartile: 3rd data value Qi = 43 Third Quartile: 8th data value Qa = 52

Interquartile range is So lower fence: 1 1.5IQR 43-1.5.9 29.5 Upper fence: Q3 1.5IQR 521.5 9 65.5 There is only one data value outside the range (29.5, 65.5). There if one outlier 105.

Following table shows the calculations for mean and standard deviaton: (x-mean) (x-mean)*2 43 0.1936 0.44 37 6.44 41.4736 50 6.56 43.0336 7.56 51 57.1536 58 14.56 211.9936 52 8.56 73.2736 45 1.56 2.4336 1.56 45 2.4336 10 33.44 1118.2336 Total 391 1550.2224 Mean ΣΧ 391 = 43.44 9 Standard deviation - 13.92

Following is the ordered data set: 10 37 43 45 45 50 51 52 58 Median: 5th data value: Median45 First Quartile: 3rd data value Q1 43 Third Quartile: 7th data value 3 51