Question

Using the following distribution, calculate the following measures of central tendency:

Answer 1

Answer:

(a) Residents

(b) $Median = 0.13$

(c)  $\bar x = 0.14$

(d) Right skewed

Step-by-step explanation:

Given

The data of residents without health insurance

Solving (a): The variable

The variable is the residents

Solving (b): The median

First, we sort the data

$Sorted: 0.09, 0.10, 0.11, 0.13, 0.13, 0.14, 0.16, 0.19, 0.25$

So, the median position is:

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

$Median = \frac{9 + 1}{2}$

$Median = \frac{10}{2}$

$Median = 5th$

The 5th element of the dataset is: 0.13

So:

$Median = 0.13$

Solving (c): The mean

This is calculated as:

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

$\bar x = \frac{0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25}{9}$

$\bar x = \frac{1.3}{9}$

$\bar x = 0.14$

Solving (d): The shape of the distribution

In (b) and (c), we have:

$Median = 0.13$

$\bar x = 0.14$

By comparison, the mean is greater than the median.

Hence, the shape is: right skewed.