Question

A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights, blankets, and so forth) in their vehicles for emergency use while driving in winter. The following data give the number of items out of these 12 that were carried in their vehicles by 15 randomly selected motorists.
5.3 78 0 105 12 10 7 6 7 119
Find the mean, median, and mode for these data. Round your answers to two decimal places, where appropriate.
Mean items
Median items
Mode - items

Answer 1

Answer:

$Mean = 6.07$

$Median = 7$

$Mode = 7$

Step-by-step explanation:

Given

$Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9$

$n = 15$

Solving (a): The mean

Mean is calculated as:

$Mean = \frac{\sum x}{n}$

This gives:

$Mean = \frac{5+ 3+ 7+ 8+ 0+ 1+ 0+ 5+ 12+ 10+ 7+ 6+ 7+ 11+ 9}{15}$

$Mean = \frac{91}{15}$

$Mean = 6.07$

Solving (b): The median

Sort the data in ascending order:

$Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9$

$Sorted: 0\ 0\ 1\ 3\ 5\ 5\ 6\ 7\ 7\ 7\ 8\ 9\ 10\ 11\ 12$

The median is:

$Median = \frac{n + 1}{2}th$

$Median = \frac{15 + 1}{2}th$

$Median = \frac{16}{2}th$

$Median = 8th$    

The 8th item on the sorted dataset is 7; So:

$Median = 7$

Solving (c): The mode

$Mode = 7$

Because it has a frequency of 3 (more than any other element of the dataset).