Question

find the mean age of the celebrities. using the mean age, find the mad (mean absolute deviation).

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a set of data $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 5$, $x_1=19$, $x_2 = 60$, $x_3=25$, $x_4=33$, $x_5=28$.
$\sum_{i=1}^{5}x_i=19 + 60+25 + 33+28=165$
$\bar{x}=\frac{165}{5}=33$

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 $x_1 = 19$: $|19 - 33|=14$
For $x_2 = 60$: $|60 - 33|=27$
For $x_3 = 25$: $|25 - 33|=8$
For $x_4 = 33$: $|33 - 33|=0$
For $x_5 = 28$: $|28 - 33|=5$

Step3: Calculate the MAD

The formula for the Mean Absolute Deviation (MAD) is $MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i = 1}^{5}|x_i-\bar{x}|=14 + 27+8+0 + 5=54$
$MAD=\frac{54}{5}=10.8$

Answer:

$10.8$