Question

dataset ii: 3 5 8 7 9
e) the median of dataset ii is: 7
f) the iqr of dataset ii is from 4 to 8.5
g) the mean of dataset ii is: 6.4
h) the standard deviation of dataset ii is: enter an integer or decimal number more...
question help: video

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 mean of the dataset and \(n\) is the number of data points.

Step2: Identify values

The dataset is \(3,5,8,7,9\), \(n = 5\), and \(\bar{x}=6.4\) (already calculated in part g).

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

For \(x_1 = 3\): \((3 - 6.4)^2=(-3.4)^2 = 11.56\)
For \(x_2 = 5\): \((5 - 6.4)^2=(-1.4)^2 = 1.96\)
For \(x_3 = 8\): \((8 - 6.4)^2=(1.6)^2 = 2.56\)
For \(x_4 = 7\): \((7 - 6.4)^2=(0.6)^2 = 0.36\)
For \(x_5 = 9\): \((9 - 6.4)^2=(2.6)^2 = 6.76\)

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

\(\sum_{i = 1}^{5}(x_i-\bar{x})^2=11.56 + 1.96+2.56 + 0.36+6.76=23.2\)

Step5: Calculate the standard - deviation

\(s=\sqrt{\frac{23.2}{5 - 1}}=\sqrt{\frac{23.2}{4}}=\sqrt{5.8}\approx2.41\)

Answer:

\(2.41\)