Answer:
Step-by-step explanation:
The mean for 2018 scores is:
[tex]M ean ( \overline X) = \dfrac{\sum x_i}{n}[/tex]
[tex]M ean ( \overline X) = \dfrac{74 + 78+79+77+75+73+75+77}{8}[/tex]
[tex]M ean ( \overline X) = \dfrac{608} {8}[/tex]
[tex]\mathbf{M ean ( \overline X) = 76}[/tex]
The standard deviation for 2018 scores is:
[tex]s = \sqrt{\dfrac{\sum ( x_i - \bar x)^2}{n- 1} }[/tex]
[tex]s = \sqrt{\dfrac{ ( 74 -76)^2+( 78 -76)^2+( 79 -76)^2+...+( 73 -76)^2+( 75 -76)^2+( 77 -76)^2}{8- 1} }[/tex]
[tex]s = \sqrt{\dfrac{30}{7} }[/tex]
s = 2.07
The mean and standard deviation for the year 2018 scores is:
2018
Mean 76
Standard deviation 2.07
The mean for 2019 scores is:
[tex]M ean ( \overline X) = \dfrac{\sum x_i}{n}[/tex]
[tex]M ean ( \overline X) = \dfrac{71 + 70+75+77+85+80+71+79}{8}[/tex]
[tex]M ean ( \overline X) = \dfrac{608} {8}[/tex]
[tex]\mathbf{M ean ( \overline X) = 76}[/tex]
The standard deviation for 2019 scores is:
[tex]s = \sqrt{\dfrac{\sum ( x_i - \bar x)^2}{n- 1} }[/tex]
[tex]s = \sqrt{\dfrac{ ( 71 -76)^2+( 70 -76)^2+( 75-76)^2+...+( 80 -76)^2+( 71 -76)^2+( 79 -76)^2}{8- 1} }[/tex]
[tex]s = \sqrt{\dfrac{194}{7} }[/tex]
s = 5.26
The mean and standard deviation for the year 2019 scores is:
2019
Mean 76
Standard deviation 5.26
Difference: Both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.
Thus, the variation in scores was higher in 2019.
