# Assume the following daily closing for the Dow Jones Industrial Average:

Day DJIA Day DJIA
1 12,010 7 12,220
2 12,100 8 12,130
3 12,165 9 12,250
4 12,080 10 12,315
5 12,070 11 12,240
6 12,150 12 12,310

a. calculate a four-day moving average for Days 4 through 12.
b. Assume that the index on day 13 closes at 12,300. would this signal a buy or sell decision?

Please show me the calculation steps.Thanks

This site has a good explanation of the steps needed to calculate the moving average.

http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averages

Since 12,300 is above the moving average, you could sell to lock in a profit.

## To calculate the four-day moving average for Days 4 through 12, you need to sum the closing values for each day and divide it by the number of days considered.

First, let's take the closing values for Days 4 through 12:
Day 4: 12,080
Day 5: 12,070
Day 6: 12,150
Day 7: 12,220
Day 8: 12,130
Day 9: 12,250
Day 10: 12,315
Day 11: 12,240
Day 12: 12,310

12,080 + 12,070 + 12,150 + 12,220 + 12,130 + 12,250 + 12,315 + 12,240 + 12,310 = 109,765

Now, divide the sum by the number of days, which is 9:
109,765 / 9 = 12,196.11

So, the four-day moving average for Days 4 through 12 is approximately 12,196.11.

For part b, let's consider that Day 13 has a closing value of 12,300. To determine if this signals a buy or sell decision, compare it with the four-day moving average.

Since 12,300 is above the moving average (12,196.11), it indicates that the index is performing better than the average. This could be interpreted as a signal to buy, as it suggests a potential upward trend in the index.

## To calculate the four-day moving average for Days 4 through 12, follow these steps:

Step 1: Add up the closing values for Days 4 through 7.

12,080 + 12,070 + 12,150 + 12,220 = 48,520

Step 2: Divide the sum by 4 (the number of days included in the moving average).

48,520 / 4 = 12,130

Step 3: Repeat steps 1 and 2 for the subsequent days in the range.

Day 8:
12,130 + 12,130 + 12,165 + 12,100 = 48,525
48,525 / 4 = 12,131.25

Day 9:
12,131.25 + 12,165 + 12,100 + 12,250 = 48,646.25
48,646.25 / 4 = 12,161.56

Day 10:
12,161.56 + 12,250 + 12,315 + 12,240 = 48,966.56
48,966.56 / 4 = 12,241.64

Day 11:
12,241.64 + 12,315 + 12,240 + 12,240 = 49,036.64
49,036.64 / 4 = 12,259.16

Day 12:
12,259.16 + 12,240 + 12,310 + 12,240 = 48,049.16
48,049.16 / 4 = 12,012.29

So, the four-day moving averages for Days 4 through 12 are as follows:

Day 4: 12,130
Day 5: 12,131.25
Day 6: 12,161.56
Day 7: 12,241.64
Day 8: 12,259.16
Day 9: 12,012.29

Now, let's move on to the second part of the question:

Assuming that the index on Day 13 closes at 12,300, we compare it to the four-day moving average.

The four-day moving average on Day 13 would be the average of Days 10, 11, 12, and 13:

12,250 + 12,240 + 12,310 + 12,300 = 48,100
48,100 / 4 = 12,025

Since 12,300 is above the moving average of 12,025, this could signal a buy decision as it indicates that the average has increased and there may be an upward trend.