Question

Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7-week period?

• A. $64
• B. $70
• C. $73
• D. $74
• E. $85

Hint:

To calculate the average of a set of numbers more quickly, you can use the "assumed mean" method. Guess a mean (e.g., $70, as it's near the middle). Then, find the sum of the differences from this assumed mean: `(4) + (-1) + (-6) + (9) + (-6) + (14) + (7) = 21`. Divide this sum of differences by the number of values: `21 / 7 = 3`. Add this result to your assumed mean: `70 + 3 = 73`.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We are asked to find the arithmetic mean (average) of a set of weekly grocery bills. The arithmetic mean is the sum of all values divided by the number of values.

Step 2: Key Formula or Approach:
\[ \text{Average (Mean)} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

Step 3: Detailed Explanation:
The given weekly grocery bills are: 74, 69, 64, 79, 64, 84, and 77.

Step 3a: Find the sum of all values:
\[ 74 + 69 + 64 + 79 + 64 + 84 + 77 \] Group for easier addition:
\[ (74+77) + (69+79) + (64+64) + 84 \] \[ 151 + 148 + 128 + 84 \] \[ 511 \] So, the total sum = 511.

Step 3b: Count the number of values:
There are 7 weekly bills.

Step 3c: Calculate the mean:
\[ \text{Average} = \frac{511}{7} = 73 \]

Step 4: Final Answer:
The Smiths’ average weekly grocery bill over the 7-week period was $73.