Question

x
1.3
6.5
5.5
5.6
18.8
10
25.8
standard deviation, s: round to two decimal places. enter an integer or decimal number more..
variance, s²: round to one decimal place.
submit question

Explanation:

Step1: Calculate the mean

The data set is \(x = \{1.3,6.5,5.5,5.6,18.8,10,25.8\}\). The mean \(\bar{x}=\frac{1.3 + 6.5+5.5+5.6+18.8+10+25.8}{7}=\frac{73.5}{7}=10.5\).

Step2: Calculate the squared - differences

\((1.3 - 10.5)^2=(-9.2)^2 = 84.64\), \((6.5 - 10.5)^2=(-4)^2 = 16\), \((5.5 - 10.5)^2=(-5)^2 = 25\), \((5.6 - 10.5)^2=(-4.9)^2 = 24.01\), \((18.8 - 10.5)^2=(8.3)^2 = 68.89\), \((10 - 10.5)^2=(-0.5)^2 = 0.25\), \((25.8 - 10.5)^2=(15.3)^2 = 234.09\).

Step3: Calculate the variance

The variance \(s^{2}=\frac{84.64 + 16+25+24.01+68.89+0.25+234.09}{7 - 1}=\frac{452.88}{6}=75.5\) (rounded to one decimal place).

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{s^{2}}=\sqrt{75.48}\approx8.69\) (rounded to two decimal places).

Answer:

Standard deviation, \(s: 8.69\)
Variance, \(s^{2}: 75.5\)