Question

charlotte has saved all her receipts from buying snacks at the corner store. on her 6 receipts, the amounts spent were: $7.20 $8.00 $3.10 $4.40 $6.60 $6.70 what was the mean absolute deviation of the amounts spent? if the answer is a decimal, round it to the nearest ten cents. mean absolute deviation (mad): $

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a set of numbers $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 6$, $x_1=7.20$, $x_2 = 8.00$, $x_3=3.10$, $x_4=4.40$, $x_5=6.60$, $x_6=6.70$.
$\sum_{i=1}^{6}x_i=7.20 + 8.00+3.10 + 4.40+6.60+6.70=36.00$
$\bar{x}=\frac{36.00}{6}=6.00$

Step2: Calculate the absolute deviations

The absolute deviation of each data - point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
For $x_1 = 7.20$: $|7.20 - 6.00|=1.20$
For $x_2 = 8.00$: $|8.00 - 6.00|=2.00$
For $x_3=3.10$: $|3.10 - 6.00|=2.90$
For $x_4=4.40$: $|4.40 - 6.00|=1.60$
For $x_5=6.60$: $|6.60 - 6.00|=0.60$
For $x_6=6.70$: $|6.70 - 6.00|=0.70$

Step3: Calculate the mean absolute deviation (MAD)

The MAD is the mean of the absolute deviations.
$\text{MAD}=\frac{1.20 + 2.00+2.90 + 1.60+0.60+0.70}{6}$
$\sum_{i = 1}^{6}|x_i-\bar{x}|=1.20+2.00 + 2.90+1.60+0.60+0.70=9.00$
$\text{MAD}=\frac{9.00}{6}=1.50$

Answer:

$1.50$