Question

please find the range, sample standard deviation and inter - quartile range (iqr) of the following data set. 44 46 46 51 57 61 62 65 69 85 range = 41 (please enter an exact answer.) standard deviation (s) = (please show your answer to one decimal place.) iqr = (please enter an exact answer.) a new number, 234, is added to the data set above. please find the new range, sample standard deviation and iqr of the new data set. range = (please enter an exact answer.) standard deviation = (please show your answer to one decimal place.) iqr = (please enter an exact answer.) which measure of spread is less affected by the addition of the extreme observation? iqr standard deviation range

Explanation:

Step1: Calculate original range

Range = Max - Min = 85 - 44 = 41

Step2: Original mean (x̄)

Sum = 44+46+46+51+57+61+62+65+69+85 = 586, x̄ = 586/10 = 58.6

Step3: Original squared deviations sum

Σ(xi - x̄)² = 1454.4, s = √(1454.4/9) ≈ 12.7

Step4: Original IQR

Q1=46, Q3=65, IQR=65-46=19

Step5: New range (234 added)

New range = 234 - 44 = 190

Step6: New mean (x̄)

Sum=586+234=820, x̄=820/11≈74.55

Step7: New standard deviation

Σ(xi - x̄)²≈29422.82, s=√(29422.82/10)≈54.2

Step8: New IQR

Q1=46, Q3=69, IQR=69-46=23

Step9: Measure less affected by extreme value

IQR resists outliers.

Answer:

Original range = 41, standard deviation (s) = 12.7, IQR = 19
New range = 190, standard deviation = 54.2, IQR = 23
IQR