Question

Roberto took a sample of 5 recent matches for his favorite soccer team. Here is how many goals the team scored in each match: 0, 2, 1, 2, 5 Roberto found the mean was xˉ=2 goals. He thinks the standard deviation is sx =(2−2)2 + (1−2)2 +(2−2)2 +(5−2)24−−−−−−−−−−−−−−−−−−−−√ What is the error in Roberto's standard deviation calculation?

Answer 1

Roberto did not include the first term of the numerator (0-2)^2 in his calculation.

The mean of the data is also known as average.

Given the set of data 0, 2, 1, 2, 5

Mean = 0+2+1+2+5/5

Mean = 10/5

Mean = 2.0

To get the standard deviation, we will use the SD formula as shown:

$\sigma=\sqrt{\frac{\sum (x-\overline x)^2}{N} }$

$\sigma =\sqrt{ \frac{(0-2)^2+(2-2)^2+(1-2)^2+(2-2)^2+(5-2)^2}{5}}\\ \sigma = \sqrt{\frac{4+0+1+0+9}{5}} \\\sigma = \sqrt{\frac{14}{5} }\\\sigma = 1.673$

Comparing this with Roberto's calculation, we can see that Roberto did not include the first term of the numerator (0-2)^2 in his calculation.

Learn more here: brainly.com/question/10557301