Respuesta :
Answer:
(a) 48
(b) The mean is on the right side of the median
(c) 39
(d) 21.5
(e) The median salary would increase to 51
The interquartile range will remain as 21.5
The standard deviation remains the same
Step-by-step explanation:
28, 31, 34, 35, 37, 41, 42, 42, 42, 47, 49, 51, 52, 52, 60, 61, 67, 72, 75, 77.
(a) From the above data, the median salary is the average salary of the 10th and 11th salary, that is (47 + 49)/2 = 48
(b) Based on the information that the histogram of the salaries is skewed right, it means that the mean is on the right side of the median
The average is calculated as 49.75
(c) The first quartile is the middle number between the median and the smallest number that is (37 + 41)/2 = 39
(d) The interquartile range is the difference between the third and first quartiles, that is Q₃ - Q₁ = (60 + 61)/2 - 39 = 21.5
(e) The median salary would increase to (50 + 52)/2 = 51
The interquartile range of the salaries will be Q₁ = (40 + 44)/2 = 42
Q₃ = (63 + 64)/2 = 63.5
Q₃ - Q₁ = 21.5 therefore, the interquartile range will remain the same
The standard deviation of the salaries is given by [tex]\sqrt{\frac{\Sigma (x-\bar x)}{n} }[/tex]
Whereby we have [tex]\bar x = \frac{\Sigma x}{n}[/tex]
When ∑x increases by 3·n, [tex]\bar x[/tex] increases by 3 therefore the standard deviation remains the same.
