Question

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

State Proportion of Residents Without Health Insurance Louisiana 0.19 New Jersey 0.13 New York 0.16 Pennsylvania 0.11 Rhode Island 0.09 South Carolina 0.13 Texas 0.25 Washington 0.14 Wisconsin 0.10
N = 9
Identify the variable:
Identify the median:
Identify the mean:
How would you describe the shape of the distribution:

Answer 1

(a) Residents

(b)
`Median = 0.13`

(c)
`\bar x = 0.14`

(d) Right skewed

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 = (n + 1)/(2)`

`Median = (9 + 1)/(2)`

`Median = (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 = (\sum x)/(n)`

`\bar x = (0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25)/(9)`

`\bar x = (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.