Question

d. each score is divided by a constant value of 50.

1. in 2016, the 50th percentile score for household income in the united states was $59,039. what statistic for central tendency is this?
2. find the median for the following set of scores: 1, 9, 3, 6, 4, 3, 11, 10 mdn=5

Explanation:

Question 20

The 50th percentile of a dataset is the value where 50% of the data is below it and 50% is above it. The median is defined as the middle value of a dataset (or the average of the two middle values for an even - numbered dataset), and it is also the 50th percentile. So the 50th percentile score for household income is the median.

Step 1: Order the data set

First, we need to arrange the given set of scores \(1, 9, 3, 6, 4, 3, 11, 10\) in ascending order.
When we sort them, we get \(1, 3, 3, 4, 6, 9, 10, 11\).

Step 2: Find the middle value(s)

The number of data points \(n = 8\), which is an even number. For an even - numbered dataset, the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+ 1)\)-th values.
\(\frac{n}{2}=\frac{8}{2}=4\) and \(\frac{n}{2}+1 = 4 + 1=5\).
The 4th value in the ordered set is \(4\) and the 5th value is \(6\).

Step 3: Calculate the median

The median is the average of these two values. So we calculate \(\frac{4 + 6}{2}\).
\(\frac{4+6}{2}=\frac{10}{2}=5\).

Answer:

Median

Question 21