Question

#9 - adv algebra financial applications: unit 1, lesson 4, day 2 - simple moving averages
learning target: i can interpret & apply simple moving averages (sma) to analyze stock market trends.
warm - up: work independently, then discuss your work with a partner. d = 65% (15 pts)
what is todays learning target? i can interpret and apply simple moving averages to analyze stock market trends
vocabulary term definition
smoothing techniques a. the sum of a set of numbers divided by the count of the numbers in that set.
simple moving average (sma) b. tools that use historical data to identify trends after they have already begun.
arithmetic average (mean) c. statistical methods used to reduce the effects of rapid price changes.
lagging indicators d. a moving average calculated over a shorter time period, making it more responsive to recent price changes.
crossover e. the average closing price of a stock over a set period of time.
fast moving average f. a moving average calculated over a longer time period, making it less responsive to recent price changes and better for identifying long - term trends.
slow moving average g. when a faster moving average line intersects a slower moving average line on a chart, which can signal a change in a trend.

1. determine the 3 - day sma for the ten consecutive day closing prices of sprint nextel corp listed below. $7.78, $8.08, $7.99, $8.02, $7.89, $8.72, $9.19, $9.16, $8.98, $9.38
2. determine the 5 - day sma for the ten consecutive day closing prices for mastercard inc listed below. $242.50, $273.98, $278.16, $293.94, $285.04 $290.80, $296.02, $291.01, $293.41, $286.85

Explanation:

Step1: Recall SMA formula

Simple - moving - average (SMA) for $n$ days is calculated as $\text{SMA}_n=\frac{\sum_{i = 0}^{n - 1}P_{t - i}}{n}$, where $P_{t - i}$ is the price on day $t - i$.

Step2: Calculate 3 - day SMA for Sprint Nextel Corp

For the first 3 - day SMA (using prices $P_1 = 7.78$, $P_2=8.08$, $P_3 = 7.99$):
$\text{SMA}_3=\frac{7.78 + 8.08+7.99}{3}=\frac{23.85}{3}=7.95$
For the second 3 - day SMA (using prices $P_2 = 8.08$, $P_3 = 7.99$, $P_4=8.02$):
$\text{SMA}_3=\frac{8.08 + 7.99+8.02}{3}=\frac{24.09}{3}=8.03$
Continuing this way for all possible 3 - day periods in the 10 - day data set.

Step3: Calculate 5 - day SMA for MasterCard Inc

For the first 5 - day SMA (using prices $P_1 = 242.50$, $P_2=273.98$, $P_3 = 278.16$, $P_4=293.94$, $P_5 = 285.04$):
$\text{SMA}_5=\frac{242.50+273.98 + 278.16+293.94+285.04}{5}=\frac{1373.62}{5}=274.724$
For the second 5 - day SMA (using prices $P_2 = 273.98$, $P_3 = 278.16$, $P_4=293.94$, $P_5 = 285.04$, $P_6 = 290.80$):
$\text{SMA}_5=\frac{273.98+278.16 + 293.94+285.04+290.80}{5}=\frac{1321.92}{5}=264.384$
Continuing this way for all possible 5 - day periods in the 10 - day data set.

Answer:

The 3 - day SMA values for Sprint Nextel Corp and 5 - day SMA values for MasterCard Inc are calculated as shown above for each relevant period in their respective 10 - day data sets.

For the vocabulary part:
smoothing techniques: C
simple moving average (SMA): E
arithmetic average (mean): A
lagging indicators: B
crossover: G
fast moving average: D
slow moving average: F