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Answer :
We are given the closing prices:
[tex]$$56,\ 61,\ 50,\ 57,\ 60,\ 58,\ 57$$[/tex]
and we need to calculate the 4-day simple moving average (SMA).
A 4-day moving average is calculated by taking the sum of 4 consecutive closing prices and then dividing by 4. We will form four 4-day windows as follows:
1. First window (days 1–4):
The prices are [tex]$56$[/tex], [tex]$61$[/tex], [tex]$50$[/tex], and [tex]$57$[/tex].
The average is calculated as:
[tex]$$
\text{SMA}_1 = \frac{56 + 61 + 50 + 57}{4} = \frac{224}{4} = 56.
$$[/tex]
2. Second window (days 2–5):
The prices are [tex]$61$[/tex], [tex]$50$[/tex], [tex]$57$[/tex], and [tex]$60$[/tex].
The average is:
[tex]$$
\text{SMA}_2 = \frac{61 + 50 + 57 + 60}{4} = \frac{228}{4} = 57.
$$[/tex]
3. Third window (days 3–6):
The prices are [tex]$50$[/tex], [tex]$57$[/tex], [tex]$60$[/tex], and [tex]$58$[/tex].
The average is:
[tex]$$
\text{SMA}_3 = \frac{50 + 57 + 60 + 58}{4} = \frac{225}{4} = 56.25.
$$[/tex]
4. Fourth window (days 4–7):
The prices are [tex]$57$[/tex], [tex]$60$[/tex], [tex]$58$[/tex], and [tex]$57$[/tex].
The average is:
[tex]$$
\text{SMA}_4 = \frac{57 + 60 + 58 + 57}{4} = \frac{232}{4} = 58.
$$[/tex]
Thus, the sequence of 4-day SMA values is:
[tex]$$[56,\ 57,\ 56.25,\ 58].$$[/tex]
Comparing this with the answer options, we find that the correct option is:
c. \[tex]$56, \$[/tex]57, \[tex]$56.25, \$[/tex]58.
[tex]$$56,\ 61,\ 50,\ 57,\ 60,\ 58,\ 57$$[/tex]
and we need to calculate the 4-day simple moving average (SMA).
A 4-day moving average is calculated by taking the sum of 4 consecutive closing prices and then dividing by 4. We will form four 4-day windows as follows:
1. First window (days 1–4):
The prices are [tex]$56$[/tex], [tex]$61$[/tex], [tex]$50$[/tex], and [tex]$57$[/tex].
The average is calculated as:
[tex]$$
\text{SMA}_1 = \frac{56 + 61 + 50 + 57}{4} = \frac{224}{4} = 56.
$$[/tex]
2. Second window (days 2–5):
The prices are [tex]$61$[/tex], [tex]$50$[/tex], [tex]$57$[/tex], and [tex]$60$[/tex].
The average is:
[tex]$$
\text{SMA}_2 = \frac{61 + 50 + 57 + 60}{4} = \frac{228}{4} = 57.
$$[/tex]
3. Third window (days 3–6):
The prices are [tex]$50$[/tex], [tex]$57$[/tex], [tex]$60$[/tex], and [tex]$58$[/tex].
The average is:
[tex]$$
\text{SMA}_3 = \frac{50 + 57 + 60 + 58}{4} = \frac{225}{4} = 56.25.
$$[/tex]
4. Fourth window (days 4–7):
The prices are [tex]$57$[/tex], [tex]$60$[/tex], [tex]$58$[/tex], and [tex]$57$[/tex].
The average is:
[tex]$$
\text{SMA}_4 = \frac{57 + 60 + 58 + 57}{4} = \frac{232}{4} = 58.
$$[/tex]
Thus, the sequence of 4-day SMA values is:
[tex]$$[56,\ 57,\ 56.25,\ 58].$$[/tex]
Comparing this with the answer options, we find that the correct option is:
c. \[tex]$56, \$[/tex]57, \[tex]$56.25, \$[/tex]58.
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