Answer:
Option 1
[tex]\bar x_1 = 96.2[/tex]
[tex]Mode = 99[/tex]
[tex]\sigma_1 = 3.22[/tex]
Option 2
[tex]\bar x_2 = 97.4[/tex]
[tex]Mode = 97[/tex]
[tex]\sigma_2 = 0.499[/tex]
Explanation:
Given
[tex]Option\ 1: 99, 98, 99, 94, 92, 99, 98, 99, 94, 90[/tex]
[tex]Option\ 2: 98, 97, 97, 97, 98, 98, 97, 97, 98[/tex]
Required
The mean, mode and standard deviation of both options
Option 1
Calculate mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x_1 = \frac{99+ 98+ 99+ 94+ 92+ 99+ 98+ 99+ 94+ 90}{10}[/tex]
[tex]\bar x_1 = \frac{962}{10}[/tex]
[tex]\bar x_1 = 96.2[/tex]
Calculate mode
[tex]Mode = 99[/tex]
Because it has a frequency of 4 (more than other element of the dataset)
Calculate standard deviation
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(99-96.2)^2 +.............+(90-96.2)^2}{10}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{103.6}{10}}[/tex]
[tex]\sigma_1 = \sqrt{10.36}[/tex]
[tex]\sigma_1 = 3.22[/tex]
Option 2
Calculate mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x_2 = \frac{98+ 97+ 97+ 97+ 98+ 98+ 97+ 97+ 98}{9}[/tex]
[tex]\bar x_2 = \frac{877}{9}[/tex]
[tex]\bar x_2 = 97.4[/tex]
Calculate mode
[tex]Mode = 97[/tex]
Because it has a frequency of 5 (more than other element of the dataset)
Calculate standard deviation
[tex]\sigma_2 = \sqrt{\frac{(98-97.4)^2+..............+ (98-97.4)^2}{9}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{2.24}{9}}[/tex]
[tex]\sigma_2 = \sqrt{0.2489}[/tex]
[tex]\sigma_2 = 0.499[/tex]
