Question

dataset ii: 3 5 6 7 20
e) the median of dataset ii is: 6
f) the iqr of dataset ii is from 4 to 13.5
g) the mean of dataset ii is: 8.2
h) the standard deviation of dataset ii is: enter an integer or decimal number more...
question help: video 1 video 2

Explanation:

Step1: Recall standard - deviation formula

The formula for the sample standard deviation of a dataset $x_1,x_2,\cdots,x_n$ is $s = \sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$, where $\bar{x}$ is the sample mean and $n$ is the number of data - points.

Step2: Identify values

The dataset is $x_1=3,x_2 = 5,x_3=6,x_4=7,x_5 = 20$, and $n = 5$. The mean $\bar{x}=8.2$.

Step3: Calculate $(x_i-\bar{x})^2$ for each $i$

For $x_1 = 3$: $(3 - 8.2)^2=(-5.2)^2 = 27.04$.
For $x_2 = 5$: $(5 - 8.2)^2=(-3.2)^2 = 10.24$.
For $x_3 = 6$: $(6 - 8.2)^2=(-2.2)^2 = 4.84$.
For $x_4 = 7$: $(7 - 8.2)^2=(-1.2)^2 = 1.44$.
For $x_5 = 20$: $(20 - 8.2)^2=(11.8)^2 = 139.24$.

Step4: Calculate $\sum_{i = 1}^{n}(x_i-\bar{x})^2$

$\sum_{i = 1}^{5}(x_i - 8.2)^2=27.04+10.24 + 4.84+1.44+139.24=182.8$.

Step5: Calculate the standard deviation

$s=\sqrt{\frac{182.8}{5 - 1}}=\sqrt{\frac{182.8}{4}}=\sqrt{45.7}\approx6.76$.

Answer:

$6.76$