Question

Customers at a sandwich shop are given a pull-tab card with every purchase, and every card is a winner. Reba has received 5 cards, with her winnings of:
$1.00$5.10$5.70$4.20$1.00
What was the mean absolute deviation of the amounts won?

If the answer is a decimal, round it to the nearest ten cents.

mean absolute deviation (MAD): $

Answer 1

To calculate the mean absolute deviation (MAD) of Reba's winnings, we first need to follow these steps:

1. **Calculate the mean (average)** of the winnings.
2. **Find the absolute deviations** from the mean.
3. **Calculate the mean of those absolute deviations**.

Let's perform these steps:

### Step 1: Calculate the Mean
Reba's winnings are:
- $1.00
- $5.10
- $5.70
- $4.20
- $1.00

First, we sum these amounts:
\[
1.00 + 5.10 + 5.70 + 4.20 + 1.00 = 17.10
\]
Next, we divide by the number of winnings (5):
\[
\text{Mean} = \frac{17.10}{5} = 3.42
\]

### Step 2: Calculate Absolute Deviations from the Mean
Now, we will calculate the absolute deviation of each amount from the mean (3.42):

1. \(|1.00 - 3.42| = | -2.42 | = 2.42\)
2. \(|5.10 - 3.42| = | 1.68 | = 1.68\)
3. \(|5.70 - 3.42| = | 2.28 | = 2.28\)
4. \(|4.20 - 3.42| = | 0.78 | = 0.78\)
5. \(|1.00 - 3.42| = | -2.42 | = 2.42\)

So, the absolute deviations are:
- 2.42
- 1.68
- 2.28
- 0.78
- 2.42

### Step 3: Calculate the Mean of Absolute Deviations
Now, we sum the absolute deviations:
\[
2.42 + 1.68 + 2.28 + 0.78 + 2.42 = 9.58
\]

Next, we calculate the mean of the absolute deviations by dividing by the number of winnings (5):
\[
\text{MAD} = \frac{9.58}{5} = 1.916
\]

### Round to Nearest Ten Cents
Finally, rounding 1.916 to the nearest ten cents gives us:
\[
\text{MAD} \approx 1.92
\]

Thus, the mean absolute deviation of Reba's winnings is:
\[
\boxed{1.92}
\]