Respuesta :
Answer:
a)Range= 25.9
b)Variance =49.344
c)Standard deviation=7.0245
Step-by-step explanation:
Data : 28.2 49.2 30.9 28.8 28.0 25.9 34.0 29.0 23.8 30.1
Maximum Value : 49.4
Minimum Value : 23.5
Range= Maximum - Minimum
Range= 49.4 -23.5 = 25.9
(b)
[tex]Mean=\bar{x}=\frac{\sum x}{n}=\frac{309.2}{10}=30.92\\\\Variance=s^{2}=\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}=49.344[/tex]
(c) Sample standard deviation:
[tex]s=\sqrt{\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}}=7.0245[/tex]
d)s2 using the shortcut method.
X [tex]X^2[/tex]
28.6 817.96
49.4 2440.36
30.3 918.09
28.2 795.24
28.9 835.21
26.4 696.96
33.8 1142.44
29.9 894.01
23.5 552.25
30.2 912.04
Total 309.2 10004.56
[tex]s=\sqrt{\frac{\sum x^{2}_{i}-\frac{\left ( \sum x_{i} \right )^{2}}{n}}{n-1}}\\s=\frac{10004.56-\frac{309.2^{2}}{10}}{9}\\s=7.0245[/tex]
