The table below shows the total number of registered votes and valid votes in two blocks (A and B) for the years 2012 and 2015.

| Year | Registered Votes in Block A | Registered Votes in Block B | Valid Votes in Block A | Valid Votes in Block B |
|-------|-----------------------------|-----------------------------|------------------------|------------------------|
| 2012 | 750 | 1200 | 200 | 1000 |
| 2015 | 900 | 1300 | 720 | 1000 |

Note: Number of registered votes = Number of valid votes + Number of invalid votes.

**Question:**

Find the difference between the average number of invalid votes in both blocks in 2012 and the average number of invalid votes in both blocks in 2015.

Question

The table below shows the total number of registered votes and valid votes in two blocks (A and B) for the years 2012 and 2015.

| Year | Registered Votes in Block A | Registered Votes in Block B | Valid Votes in Block A | Valid Votes in Block B |
|-------|-----------------------------|-----------------------------|------------------------|------------------------|
| 2012  | 750                         | 1200                        | 200                    | 1000                   |
| 2015  | 900                         | 1300                        | 720                    | 1000                   |

Note: Number of registered votes = Number of valid votes + Number of invalid votes.

**Question:**

Find the difference between the average number of invalid votes in both blocks in 2012 and the average number of invalid votes in both blocks in 2015.

Accepted Answer

**Solution:**

1. Calculate the number of invalid votes for each block and year using the formula:
   $$	ext{Invalid votes} = 	ext{Registered votes} - 	ext{Valid votes}$$

- For 2012:
     - Block A: $750 - 200 = 550$
     - Block B: $1200 - 1000 = 200$

- For 2015:
     - Block A: $900 - 720 = 180$
     - Block B: $1300 - 1000 = 300$

2. Find the average number of invalid votes for both blocks in each year:
   - 2012 average:
     $$\frac{550 + 200}{2} = \frac{750}{2} = 375$$
   - 2015 average:
     $$\frac{180 + 300}{2} = \frac{480}{2} = 240$$

3. Calculate the difference between these averages:
   $$375 - 240 = 135$$

**Answer:** 135

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