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Given the scores of the following students: 75,71,78,80,80,81,03,04,87,00,09,91,92,94,95,96. Find the range, average deviation, variance, and standard deviation.


Sagot :

Step-by-step explanation:

The grade of 10 students in statistics are 85, 70, 89, 84, 90, 92, 75, 81, 78 and 87. What is the range, mean and the standard deviation?

A. Range= 92- 70

answer = 22

B. Mean= sum of grades / # of students

Mean= 831/10

Mean= 83.1

C. Standard deviation = S square = the sum of x square - the sum of ( x square/ # of students)/ # of student - 1

which would work out like this:

number of students= 10

sum of x squared= 85*85=7225+70*70=4900+89*89=7921+84*84=7056+90*90=8100+92*92=8464+75*75=5625+81*81=6561+78*78=6084+87*87=7569.

Answer= 69,505

sum of x = 85+70+89+84+90+92+75+81+78+87

Ans = 831

(sum of x) squared / number of students=

831*831 =690561/10

answer= 69056.1

S square = the sum of x squared - the sum of ( x square/ # of students)/ # of student - 1

S square = 69505–69056.1/10–1

S square = 448.9/9

S square = 49.88

find the square root of 49.88

therefore standard deviation is:

Answer= 7.06