Question

A group of 10 students received the following marks for a test: 58, 89,65, 78, 55,26,93,46,43,59. The standard deviation of their marks is (to two decimal places)

Answer 1

Answer:19.84

Step-by-step explanation:

S. D = √(Variance)

To find the standard deviation, we need to first find the variance

variance = ∑(x-x⁻)² / n

where x⁻ = mean

n=no. of data = 10

∑ means summation

again, we to find the mean

mean(x⁻) = 58+89+65+78+55+26+93+46+43+

59 /10

=612/10

=61.2

mean(x⁻) =61.2

x x⁻ (x-x⁻)²

58 61.2 10.24

89 61.2 772.84

65 61.2 14.44

78 61.2 282.24

55 61.2 38.44

26 61.2 1239.04

93 61.2 1011.24

46 61.2 231.04

43 61.2 331.24

59 61.2 4.84

∑(x-x⁻)² = 10.24+772.84+14.44+282.24+38.44+1239.04+1011.24+231.04+331.25+ 4.84 = 3935.6

variance = ∑(x-x⁻)² / n

=3935.6 / 10

=393.56

variance = 393.56

S. D = √(Variance)

=√(393.56)

=19.8383

S.D = 19.84 to two decimal place

Therefore the standard deviation is 19. 84