Let's begin by finding the mean of the data
[tex]\begin{gathered} \text{Mean = }\frac{\sum x}{n}=\text{ }\frac{46\text{ + 47 + }5\text{6 + 48 + }46\text{ + 52 + }5\text{7 + 52 + 4}5}{9} \\ \text{Mean = }\frac{449}{9}=48.89\text{ }\approx\text{ 48.9} \end{gathered}[/tex]
Mean = 48.9
Next, we calculate the absolute value of the difference between each data value and the mean, we have:
|data value – mean|
|46 - 48.9| = 2.9
|47 - 48.9| = 1.9
|56 - 48.9| = 7.1
|48 - 48.9| = 0.9
|46 - 48.9| = 2.9
|52 - 48.9| = 3.1
|57 - 48.9| = 8.1
|52 - 48.9| = 3.1
|45 - 48.9| = 3.9
Next, we sum up the absolute values of the differences (from above) & divide by the number of data values, we have:
[tex]\begin{gathered} MOD=\frac{2.9\text{ + 1.9 + 7.1 + 0.9 + 2.9 + 3.1 + 8.1 + 3.1 + 3.9}}{9}=\frac{69}{9} \\ \text{MOD = 7.7 }\approx\text{ 8 (to the nearest whole number)} \end{gathered}[/tex]
MOD = 8 (to the nearest whole number)
