Question

for exercise 10, use the description and table to answer the question.
stem connection the first artificial satellite was launched into space in 1957. since then, thousands of satellites have been launched. the table shows the number of satellites currently in orbit for 12 countries.

1. four other countries have the following number of satellites in orbit: 13, 22, 1, and 10. would the inclusion of data for these four countries increase or decrease the median number of satellites in orbit? how do you know?

table: number of satellites in orbit with two rows: first row 5, 10, 15, 6, 8, 13; second row 8, 7, 3, 14, 2, 17

Explanation:

Step1: Find original data set and median

First, list the original 12 data points from the table: 2, 3, 5, 6, 7, 8, 8, 10, 13, 14, 15, 17.
Since there are 12 (even) values, the median is the average of the 6th and 7th values.
6th value: \( 8 \), 7th value: \( 8 \).
Median (original) = \( \frac{8 + 8}{2} = 8 \).

Step2: Include new data and find new median

Add the four new data points: 1, 10, 13, 22. Now the data set has \( 12 + 4 = 16 \) values.
Sort the combined data: 1, 2, 3, 5, 6, 7, 8, 8, 10, 10, 13, 13, 14, 15, 17, 22.
For 16 (even) values, the median is the average of the 8th and 9th values.
8th value: \( 8 \), 9th value: \( 10 \).
Median (new) = \( \frac{8 + 10}{2} = 9 \).

Step3: Compare medians

Original median: \( 8 \), New median: \( 9 \). Since \( 9 > 8 \), the median increases.

Answer:

The inclusion of the four countries' data will increase the median. We know this because the original median (for 12 countries) was 8, and the new median (for 16 countries) is 9, so the median value rises.