Question

using the given set of data complete the following table. data set {5, 6, 8, 11, 12, 14, 19}. note: solve up to two decimal places only. mean median mean absolute deviation(mad)

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 7$, and the data - set is $\{5,6,8,11,12,14,19\}$. So, $\sum_{i=1}^{7}x_i=5 + 6+8 + 11+12+14+19=75$, and $\bar{x}=\frac{75}{7}\approx10.71$.

Step2: Calculate the absolute deviations

The absolute deviation of each data - point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
$|5 - 10.71|=5.71$, $|6 - 10.71| = 4.71$, $|8 - 10.71|=2.71$, $|11 - 10.71| = 0.29$, $|12 - 10.71|=1.29$, $|14 - 10.71| = 3.29$, $|19 - 10.71|=8.29$.

Step3: Calculate the Mean Absolute Deviation (MAD)

The formula for MAD is $MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$. $\sum_{i=1}^{7}|x_i - \bar{x}|=5.71+4.71+2.71+0.29+1.29+3.29+8.29 = 26.29$. So, $MAD=\frac{26.29}{7}\approx3.76$.

Answer:

Mean: $10.71$, Median: $11$, Mean Absolute Deviation (MAD): $3.76$