Question

There is a theory that children wearing superhero costumes are more likely to harm themselves because of the unrealistic impressions of invincibility that these costumes could create. Below there is data about the severity of injury (on a scale from 0, no injury, to 100, death) for children reporting to the emergency center at hospitals and information on which superhero costumes they were wearing (Spiderman, Superman, Batman).
Spiderman Superman Batman
55 68 26
31 32 47
58 85 30
20 69 35
47 58 53
37 52 43

Compute the following descriptive statistics for each group. (30 points total)
a. Mean
b. Sample size (n) for each group
c. Standard Deviation
d. Square root of n
e. Standard error of the mean (SEM)

Answer 1

Answer:

$Mean = 47$

$n = 6$

$s= 16.56$

$\sqrt n = 2.45$

$SEM = 11.55$

Step-by-step explanation:

Given: The above data

Solving (a): Mean of each group

Mean is calculated as:

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

$Mean = \frac{55 + 31 + 58 + 20 + 47 + 37+68 + 32 + 85 + 69 +58 + 52+26 + 47 + 30 +35 + 53 + 43}{18}$

$Mean = \frac{846}{18}$

$Mean = 47$

Solving (b): The sample size of each group

This is the number of rows in each group.

Hence:

$n = 6$

Solving (c): Standard deviation (s)

This is calculated as:

$s = \sqrt{\frac{\sum (x - \bar x)^2}{N}}$

So, we have:

$s= \sqrt{\frac{(55 - 47)^2 + (31 - 47)^2 +......... + (43 - 47)^2}{18}}$

$s= \sqrt{\frac{4936}{18}}$

$s= \sqrt{274.22}$

$s= 16.56$

Solving (d): Square root of n

$\sqrt n = \sqrt 6$

$\sqrt n = 2.45$

Solving (e): SEM

This is calculated as:

$SEM = \frac{s}{\sqrt N}$

$SEM = \frac{47}{\sqrt{16.56}}$

$SEM = \frac{47}{4.07}$

$SEM = 11.55$