Carcass wrote:
Nine job applicants have 2, 3, 4, 5, 5, 5, 6, 7, and 8 years of work experience. Find the standard deviation and interquartile range.
2, 3, 4, 5, 5, 5, 6, 7, 8
IQR = Q3 - Q1
Find the Median (Q2) first,
2, 3, 4, 5,
5, 5, 6, 7, 8
Now, find Q1 and Q3 by again finding the median on left and right side of Median (Q2),
2, 3 / 4, 5,
5, 5, 6 / 7, 8
Q1 =
3+42=3.5 and Q3 =
6+72=6.5So, IQR = 6.5 - 3.5 = 3
Now, Standard Deviation is given by
\sqrt{\frac{Σ(x_n - μ)^2}{n}}Where,
μ = Mean
x_n = numbers in given data
μ =
\frac{45}{9} = 5(x_n - μ) values: (2 - 5), (3 - 5), (4 - 5), (5 - 5), (5 - 5), (5 - 5), (6 - 5), (7 - 5), (8 - 5) = -3, -2, -1, 0, 0, 0, 1, 2, 3
(x_n - μ)^2 values: 9, 4, 1, 0, 0, 0, 1, 4, 9
Σ(x_n - μ)^2 values: 9 + 4 + 1 + 0 + 0 + 0 + 1 + 4 + 9 = 28
So, SD =
\sqrt{\frac{28}{9}} = 1.763