Question

hours spent on science homework hours spent on math homework

1. what is the difference in the median value for each set of data?
2. how is the science graph skewed? right

Explanation:

Sub - Question 1:

Step 1: Find the number of data points for Science Homework

Count the dots for "Hours Spent on Science Homework": \(3 + 5+3 + 1+1 + 1=14\) (wait, no, let's count again. The first column (3) at 3, 5 at 4, 3 at 5, 1 at 6, 1 at 7, 1 at 8. So total \(3 + 5+3+1 + 1+1 = 14\)? Wait, no, maybe I miscounted. Wait, the dots: at 3: 3 dots, at 4: 5 dots, at 5: 3 dots, at 6: 1, at 7: 1, at 8: 1. So total \(3 + 5+3 + 1+1 + 1=14\)? Wait, no, 3 + 5 is 8, +3 is 11, +1 is 12, +1 is 13, +1 is 14. Since there are 14 data points, the median is the average of the 7th and 8th values. Let's list the data in order. The first 3 are at 3, next 5 at 4 (so positions 4 - 8), then 3 at 5 (positions 9 - 11), then 1 at 6 (12), 1 at 7 (13), 1 at 8 (14). So the 7th and 8th values are both 4. So median for Science is 4.

Step 2: Find the number of data points for Math Homework

Count the dots for "Hours Spent on Math Homework": 1 at 2, 2 at 3, 3 at 4, 3 at 5, 2 at 6, 2 at 7, 1 at 8. Total: \(1+2 + 3+3+2 + 2+1=14\). The median is the average of the 7th and 8th values. Let's list the data: 1 at 2 (position 1), 2 at 3 (positions 2 - 3), 3 at 4 (positions 4 - 6), 3 at 5 (positions 7 - 9). So the 7th value is 5 and the 8th value is 5. So median for Math is 5.

Step 3: Calculate the difference

The difference between the medians is \(|4 - 5|=1\) (or \(5 - 4 = 1\)).

For a dot - plot, if the tail of the distribution is on the right (higher values), the graph is right - skewed. In the "Hours Spent on Science Homework" dot - plot, most of the data is on the left (lower values: 3, 4, 5) and there are a few data points on the right (6, 7, 8), so the tail is on the right, meaning it is right - skewed.

Answer:

1

Sub - Question 2: