Question

The number of wedding cards, in thousands, distributed in a certain city on each day for a week is given as follows:-
21, 35, 19, 27, 32, 22, 12.
The three days moving averages will be:

• A. 25, 28, 26, 23, 21
• B. 25, 24, 23, 27, 26
• C. 25, 27, 26, 27, 22
• D. 24, 28, 26, 22, 25

Hint:

Average each group of 3 consecutive values, sliding one day at a time. There will be 5 averages.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A three-day moving average takes the mean of three consecutive values, then slides forward by one value. With 7 values, we get \(7-3+1=5\) averages.

Step 2: First average.
\[ \frac{21+35+19}{3} = \frac{75}{3} = 25 \]

Step 3: Second average.
\[ \frac{35+19+27}{3} = \frac{81}{3} = 27 \]

Step 4: Third average.
\[ \frac{19+27+32}{3} = \frac{78}{3} = 26 \]

Step 5: Fourth and fifth averages.
\[ \frac{27+32+22}{3} = \frac{81}{3} = 27 \] \[ \frac{32+22+12}{3} = \frac{66}{3} = 22 \]

Step 6: Compare with the options.
We get 25, 27, 26, 27, 22. Option 1 has 28 as its second value, which is wrong. Option 2 has 24 as its second value, which is wrong. Option 4 starts with 24, which is wrong. Option 3 matches.

Final Answer:
The three-day moving averages are 25, 27, 26, 27, 22, which is option 3. \[ \boxed{25,\ 27,\ 26,\ 27,\ 22} \]