Respuesta :

The number of cars in 5 different parking lots are given as data points as follows:

[tex]35\text{ , 42 , 63 , 51 , 74}[/tex]

We are to determine the Mean Absolute Deviation ( MAD ). It is a statistical indicator which is used to quantify the variability of data points. We will apply the procedure of determining the ( MAD ) for the given set of data points.

Step 1: Determine the Mean of the data set

We will first determine the mean value of the data points given to us i.e the mean number of cars in a parking lot. The mean is determined by the following formula:

[tex]\mu\text{ = }\sum ^5_{i\mathop=1}\frac{x_i}{N}[/tex]

Where,

[tex]\begin{gathered} \mu\colon\text{ Mean} \\ x_i\colon\text{ Number of cars in ith parking lot} \\ N\colon\text{ Total number of parking lots} \end{gathered}[/tex]

We will use the above formulation to determine the mean value of the data set:

[tex]\begin{gathered} \mu\text{ = }\frac{35\text{ + 42 + 63 + 51 + 74}}{5} \\ \mu\text{ = }\frac{265}{5} \\ \textcolor{#FF7968}{\mu=}\text{\textcolor{#FF7968}{ 53}} \end{gathered}[/tex]

Step 2: Determine the absolute deviation

The term absolute deviation is the difference of each point in the data set from the central tendency ( mean of the data ). We determined the mean in Step 1 for this purpose.

To determine the absolute deviation we will subtract each data point from the mean value calculated above.

[tex]AbsoluteDeviation=|x_i-\mu|[/tex]

We will apply the above formulation for each data point as follows:

[tex]\begin{gathered} |\text{ 35 - 53 | , | 42 - 53 | , | 63 - 53 | , | 51 - 53 | , | 74 - 53 |} \\ |\text{ -18 | , | -11 | , | 10 | , | -2 | , | }21\text{ |} \\ \textcolor{#FF7968}{18}\text{\textcolor{#FF7968}{ , 11 , 10 , 2 , 21}} \end{gathered}[/tex]

Step 3: Determine the mean of absolute deviation

The final step is determine the mean of absolute deviation of each data point calculated in step 2. Using the same formulation in Step 1 to determine mean we will determine the " Mean Absolute Deviation ( MAD ) " as follows:

[tex]\begin{gathered} \mu_{AD}\text{ = }\frac{18\text{ + 11 + 10 + 2 + 21}}{5} \\ \mu_{AD}\text{ = }\frac{62}{5} \\ \textcolor{#FF7968}{\mu_{AD}}\text{\textcolor{#FF7968}{ = 12.4}} \end{gathered}[/tex]

Answer:

[tex]\textcolor{#FF7968}{MAD=12.4}\text{\textcolor{#FF7968}{ }}[/tex]