Solved on Dec 12, 2023

Determine which company has the least salary variability and the lowest average salaries based on the given salary ranges and means: Company A: range $\$ 47,000$ , mean $\$ 37,000$ Company B: range $\$ 56,000$ , mean $\$ 38,000$ Company C: range $\$ 50,000$ , mean $\$ 43,000$ Company D: range $\$ 48,000$ , mean $\$ 34,000$

STEP 1

Assumptions
1. The range of salaries is the difference between the highest and lowest salary in the company.
2. The mean salary is the average salary of all employees in the company.
3. Variability in salaries is typically indicated by the range; a smaller range suggests less variability.
4. The lowest salaries on average are indicated by the lowest mean salary.

STEP 2

To determine which company's salaries have the least variability, we compare the ranges of the salaries of the four companies.

STEP 3

List the ranges of the salaries for each company:
- Company A: \$47,000 - Company B: \$56,000 - Company C: \$50,000 - Company D: \$48,000

STEP 4

Identify the company with the smallest range, as this indicates the least variability in salaries.
$\min(\text{Company A}, \text{Company B}, \text{Company C}, \text{Company D}) = \min(\$47,000, \$56,000, \$50,000, \$48,000)$

STEP 5

Calculate the company with the smallest range.
$\min(\$47,000, \$56,000, \$50,000, \$48,000) = \$47,000$

STEP 6

Conclude that Company A has the least variability in salaries because it has the smallest range.
(a) Company A's salaries have the least variability.

STEP 7

To determine which company has the lowest salaries on average, we compare the mean salaries of the four companies.

STEP 8

List the mean salaries for each company:
- Company A: \$37,000 - Company B: \$38,000 - Company C: \$43,000 - Company D: \$34,000

STEP 9

Identify the company with the smallest mean salary, as this indicates the lowest salaries on average.
$\min(\text{Company A}, \text{Company B}, \text{Company C}, \text{Company D}) = \min(\$37,000, \$38,000, \$43,000, \$34,000)$

STEP 10

Calculate the company with the smallest mean salary.
$\min(\$37,000, \$38,000, \$43,000, \$34,000) = \$34,000$

STEP 11

Conclude that Company D has the lowest salaries on average because it has the smallest mean salary.
(b) Company D has the lowest salaries on average.

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STEP 1

STEP 2

To determine which company's salaries have the least variability, we compare the ranges of the salaries of the four companies.

STEP 3

List the ranges of the salaries for each company:
- Company A: \$47,000 - Company B: \$56,000 - Company C: \$50,000 - Company D: \$48,000

STEP 4

Identify the company with the smallest range, as this indicates the least variability in salaries.
$\min(\text{Company A}, \text{Company B}, \text{Company C}, \text{Company D}) = \min(\$47,000, \$56,000, \$50,000, \$48,000)$

STEP 5

Calculate the company with the smallest range.
$\min(\$47,000, \$56,000, \$50,000, \$48,000) = \$47,000$

STEP 6

Conclude that Company A has the least variability in salaries because it has the smallest range.
(a) Company A's salaries have the least variability.

STEP 7

To determine which company has the lowest salaries on average, we compare the mean salaries of the four companies.

STEP 8

List the mean salaries for each company:
- Company A: \$37,000 - Company B: \$38,000 - Company C: \$43,000 - Company D: \$34,000

STEP 9

Identify the company with the smallest mean salary, as this indicates the lowest salaries on average.
$\min(\text{Company A}, \text{Company B}, \text{Company C}, \text{Company D}) = \min(\$37,000, \$38,000, \$43,000, \$34,000)$

STEP 10

Calculate the company with the smallest mean salary.
$\min(\$37,000, \$38,000, \$43,000, \$34,000) = \$34,000$

STEP 11

Conclude that Company D has the lowest salaries on average because it has the smallest mean salary.
(b) Company D has the lowest salaries on average.

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STEP 1

STEP 2

To determine which company's salaries have the least variability, we compare the ranges of the salaries of the four companies.

STEP 3

List the ranges of the salaries for each company:- Company A: \$47,000 - Company B: \$56,000 - Company C: \$50,000 - Company D: \$48,000

STEP 4

STEP 5

Calculate the company with the smallest range.min⁡($47,000,$56,000,$50,000,$48,000)=$47,000\min(\$47,000, \$56,000, \$50,000, \$48,000) = \$47,000min($47,000,$56,000,$50,000,$48,000)=$47,000

STEP 6

Conclude that Company A has the least variability in salaries because it has the smallest range.(a) Company A's salaries have the least variability.

STEP 7

To determine which company has the lowest salaries on average, we compare the mean salaries of the four companies.

STEP 8

List the mean salaries for each company:- Company A: \$37,000 - Company B: \$38,000 - Company C: \$43,000 - Company D: \$34,000

STEP 9

STEP 10

Calculate the company with the smallest mean salary.min⁡($37,000,$38,000,$43,000,$34,000)=$34,000\min(\$37,000, \$38,000, \$43,000, \$34,000) = \$34,000min($37,000,$38,000,$43,000,$34,000)=$34,000

STEP 11

Conclude that Company D has the lowest salaries on average because it has the smallest mean salary.(b) Company D has the lowest salaries on average.

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List the ranges of the salaries for each company:
- Company A: \$47,000 - Company B: \$56,000 - Company C: \$50,000 - Company D: \$48,000

Calculate the company with the smallest range.
$\min(\$47,000, \$56,000, \$50,000, \$48,000) = \$47,000$

Conclude that Company A has the least variability in salaries because it has the smallest range.
(a) Company A's salaries have the least variability.

List the mean salaries for each company:
- Company A: \$37,000 - Company B: \$38,000 - Company C: \$43,000 - Company D: \$34,000

Calculate the company with the smallest mean salary.
$\min(\$37,000, \$38,000, \$43,000, \$34,000) = \$34,000$

Conclude that Company D has the lowest salaries on average because it has the smallest mean salary.
(b) Company D has the lowest salaries on average.