# Math 132, Project 1 – Average Changes

## Question 1:

### a. Go to Nasdaq Historical, then pick a stock and download its values over the last year. Then fill in the left column of the table below.

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|-------------------|--------------------------|---------------------------------------------|
| 1/2/2020 | | | |
| 2/3/2020 | | | |
| 3/2/2020 | | | |
| 4/1/2020 | | | |
| 5/1/2020 | | | |
| 6/1/2020 | | | |
| 7/1/2020 | | | |
| 8/3/2020 | | | |
| 9/1/2020 | | | |
| 10/1/2020 | | | |
| 11/2/2020 | | | |
| 12/1/2020 | | | |
| 1/4/2021 | | | |
| 2/1/2021 | | | |

[https://www.nasdaq.com/market-activity/quotes/historical](https://www.nasdaq.com/market-activity/quotes/historical)

<details> <summary> Example: </summary>

I used Apple (AAPL). You can't use this stock data. You must use a different one.

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|-------------------|--------------------------|---------------------------------------------|
| 1/2/2020 | 77.38 | | |
| 2/3/2020 | 68.34 | | |
| 3/2/2020 | 63.57 | | |
| 4/1/2020 | 73.45 | | |
| 5/1/2020 | 79.49 | | |
| 6/1/2020 | 91.20 | | |
| 7/1/2020 | 106.26 | | |
| 8/3/2020 | 129.04 | | |
| 9/1/2020 | 115.81 | | |
| 10/1/2020 | 108.86 | | |
| 11/2/2020 | 119.05 | | |
| 12/1/2020 | 132.69 | | |
| 1/4/2021 | 131.96 | | |
| 2/1/2021 | 121.26 | | |

</details>

### b. Fill in the next two columns by calculating the average change of the previous column. The column for the average change will have one row less, the column for the average change of the average change will have two rows less.

<details> <summary> Example: </summary>

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|--------------------|-------------------------------------|---------------------------------------------------------|
| 1/2/2020 | 77.38 | 68.34 - 77.38 = -9.04 | -4.77 - (-9.04) = 4.27 |
| 2/3/2020 | 68.34 | 63.57 - 68.34 = -4.77 | 9.88 - (-4.77) = 14.65 |
| 3/2/2020 | 63.57 | 73.45 - 63.57 = 9.88 | 6.04 - 9.88 = -3.84 |
| 4/1/2020 | 73.45 | 79.49 - 73.45 = 6.04 | 11.71 - 6.04 = 5.67 |
| 5/1/2020 | 79.49 | 91.20 - 79.49 = 11.71 | 15.06 - 11.71 = 3.35 |
| 6/1/2020 | 91.20 | 106.26 - 91.20 = 15.06 | 22.78 - 15.06 = 7.72 |
| 7/1/2020 | 106.26 | 129.04 - 106.26 = 22.78 | -13.23 - 22.78 = -36.01 |
| 8/3/2020 | 129.04 | 115.81 - 129.04 = -13.23 | -6.95 - (-13.23) = 6.28 |
| 9/1/2020 | 115.81 | 108.86 - 115.81 = -6.95 | 10.19 - (-6.95) = 17.14 |
| 10/1/2020 | 108.86 | 119.05 - 108.86 = 10.19 | 13.64 - 10.19 = 3.45 |
| 11/2/2020 | 119.05 | 132.69 - 119.05 = 13.64 | -0.73 - 13.64 = -14.37 |
| 12/1/2020 | 132.69 | 131.96 - 132.69 = -0.73 | -10.70 - (-0.73) = -9.97 |
| 1/4/2021 | 131.96 | 121.26 - 131.96 = -10.70 | |
| 2/1/2021 | 121.26 | | |

Now we can clean the table up.

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|-------------------|--------------------------|---------------------------------------------|
| 1/2/2020 | 77.38 | -9.04 | 4.27 |
| 2/3/2020 | 68.34 | -4.77 | 14.65 |
| 3/2/2020 | 63.57 | 9.88 | -3.84 |
| 4/1/2020 | 73.45 | 6.04 | 5.67 |
| 5/1/2020 | 79.49 | 11.71 | 3.35 |
| 6/1/2020 | 91.20 | 15.06 | 7.72 |
| 7/1/2020 | 106.26 | 22.78 | -36.01 |
| 8/3/2020 | 129.04 | -13.23 | 6.28 |
| 9/1/2020 | 115.81 | -6.95 | 17.14 |
| 10/1/2020 | 108.86 | 10.19 | 3.45 |
| 11/2/2020 | 119.05 | 13.64 | -14.37 |
| 12/1/2020 | 132.69 | -0.73 | -9.97 |
| 1/4/2021 | 131.96 | -10.70 | |
| 2/1/2021 | 121.26 | | |

</details>

### c. Plot the values of each column and connect the values with straight lines. Use always the same scaling of the x-axis, adjust the scale of the y-axis to the range of values.

<details> <summary> Example: </summary>

Using the data from above example in part b:




</details>

### d. Describe the relationship between the 3 plots.

<details> <summary> Example: </summary>

The rate of change is the slope of the stock price. Stock price going down means the rate of change is negative.

Rate of change of change is positive if AAPL's rate of change is increasing, and the rate of change of change is negative if the AAPL's rate of change is decreasing.

</details>

---

## Question 2:

### a. The table below shows some values for a hypothetical stock company ABC. Fill in the first two columns.

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|-------------------|--------------------------|---------------------------------------------|
| 1/2/2020 | 200 | | 2 |
| 2/3/2020 | | | 3 |
| 3/2/2020 | | | 4 |
| 4/1/2020 | | | 3 |
| 5/1/2020 | | | 2 |
| 6/1/2020 | | | 1 |
| 7/1/2020 | | | 0 |
| 8/3/2020 | | | -1 |
| 9/1/2020 | | | -2 |
| 10/1/2020 | | | -3 |
| 11/2/2020 | | | -4 |
| 12/1/2020 | | -5 | -5 |

<details> <summary> Example: </summary>

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|-------------------|--------------------------|---------------------------------------------|
| 1/2/2020 | 300 | $-1-1=-2$ | 1 |
| 2/3/2020 | $300-2=298$ | $1-2=-1$ | 2 |
| 3/2/2020 | $298-1=297$ | $4-3=1$ | 3 |
| 4/1/2020 | $297+1=298$ | $6-2=4$ | 2 |
| 5/1/2020 | $298+4=302$ | $7-1=6$ | 1 |
| 6/1/2020 | $302+6=308$ | $7-0=7$ | 0 |
| 7/1/2020 | $308+7=315$ | $6+1=7$ | -1 |
| 8/3/2020 | $315+7=322$ | $4+2=6$ | -2 |
| 9/1/2020 | $322+6=328$ | $1+3=4$ | -3 |
| 10/1/2020 | $328+4=332$ | $-3+4=1$ | -4 |
| 11/2/2020 | $332+1=333$ | $-8+5=-3$ | -5 |
| 12/1/2020 | $333-3=330$ | $-8$ | -6 |

Cleaned up:

| Date | Closing value ($) | Average Change ($/month) | Average Change of Average Change ($/month²) |
|------------|-------------------|--------------------------|---------------------------------------------|
| 1/2/2020 | 300 | -2 | 1 |
| 2/3/2020 | 298 | -1 | 2 |
| 3/2/2020 | 297 | 1 | 3 |
| 4/1/2020 | 298 | 4 | 2 |
| 5/1/2020 | 302 | 6 | 1 |
| 6/1/2020 | 308 | 7 | 0 |
| 7/1/2020 | 315 | 7 | -1 |
| 8/3/2020 | 322 | 6 | -2 |
| 9/1/2020 | 328 | 4 | -3 |
| 10/1/2020 | 332 | 1 | -4 |
| 11/2/2020 | 333 | -3 | -5 |
| 12/1/2020 | 330 | -8 | -6 |

</details>

### b. Would you be able to fill out the first two columns without the single given entries in column 1 and 2?

<details> <summary> Example: </summary>

We needed to get the 2nd to last row in the 3rd column from the last row in the 3rd column, to start and fill up the 3rd row going up.

Then we needed the first row in the 3rd column to get the next rows in the 2nd column.

Otherwise we couldn't have gotten any values.

</details>

### c. Plot the values of each column in a separate plot with the same x-axis scale.

<details> <summary> Example: </summary>

Using Microsoft Excel:




</details>

### d. Can you confirm your observation from Question 1?