Question
In: Statistics and Probability
Sample annual salaries (in thousands of dollars) for employees at a company are listed. 43, 54,...
Sample annual salaries (in thousands of dollars) for employees at a company are listed.
43, 54, 55, 51, 33, 33, 43, 54, 55, 26, 51, 43, 46
(a) Find the sample mean and sample standard deviation.
(b) Each employee in the sample is given a $3000 raise. Find the sample mean and sample standard deviation for the revised data set.
(c) Each employee in the sample takes a pay cut of $2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set.
(d) What can you conclude from the results of (a), (b), and (c)?
Solutions
Expert Solution
a)
| X | (X - X̄)² |
| 43 | 4.64 |
| 54 | 78.25 |
| 55 | 96.95 |
| 51 | 34.18 |
| 33 | 147.72 |
| 33 | 147.72 |
| 43 | 4.639 |
| 54 | 78.254 |
| 55 | 96.947 |
| 26 | 366.870 |
| 51 | 34.178 |
| 43 | 4.639 |
| 46 | 0.716 |
| X | (X - X̄)² | |
| total sum | 587 | 1095.69 |
| n | 13 | 13 |
mean = ΣX/n =
587.000 / 13 =
45.1538(thousands of dollars) = $45153.85
sample std dev = √ [ Σ(X - X̄)²/(n-1)]
= √ (1095.6923/12)
= 9.5551(thousands of dollars) =
$9555.1
b) new sample mean = 45153.85 - 3000 = 42153.85
std dev remain unchanged = 9555.1
c)
new sample mean = 45153.85 -2000 = 43153.85
std dev remain unchanged = 9555.1
d)
if each data value is increase/ decrease by a value , Sample mean decreases/ increases by same value resp.
but std dev do not change
orchestra answered 2 years agoRelated Solutions
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