measures of spread
Standard dev
volume
surface area
non-calculator
100
Find the mean of the numbers below:
18, 17, 8, 8, 9, 7
You must show full working
mean = (18 + 17 + 8 + 8 + 9 + 7) / 6
= 67 / 6
= 11.2
100
Calculate the standard deviation for the following data set:
1, 13, 17, 19, 25
The mean is 15.
S.D = (1 - 15)^2 + (13 - 15)^2 + (17 - 15)^2 + (19 - 15)^2 + (25 - 15)^2
S.D = 320 / 5
s.d. = square root 64
S.D = 8
100
Calculate the volume of the following square base pyramid
Area of base = 36
height = 6
V = (1/3) x bh
=(1/3) x 6 x 36
= 72m3
100
Calculate the surface area of the pyramid below:
area triangle = 1/2bh
= 1/2 x 10 x 11
= 55
Area square = s2
= 102
= 100cm2
SA = Area square + (4 x area of triangle)
= 100 + (4 x 55)
= 320cm2
100
Determine the mean of the following:
5, 10, 12, 3
5 + 10 + 12 + 3 = 20
20 / 4 = 5
200
Find the median of the numbers below
7, 14, 15, 9, 13, 5
9 + 13 / 2 = 11
median = 11
200
Calculate the standard deviation for the following data set:
5, 5, 7, 9, 14
Mean = 8
S.D. = (5 - 8)2 + (5 - 8)2 + (7 - 8)2 + (9 - 8)2 + (14 - 8)2
= 56 / 5
= squareroot 11.2
= 3.35
200
calculate the volume of the following square base pyramid
Area of base: 15 x 15 = 225
Volume pyramid = (1/3)bh
= (1/3) x 225 x 30
= 2250mm3
200
Calculate the surface area of the square based pyramid below:
Area of triangle = 1/2 bh
= 1/2 x 8 x 11
= 44mm2
Area of square = s2
= 82
= 64mm2
S.A. = Area square + (4 x area triangle)
= 64 + (4 x 44)
= 240mm2
200
A cylinder has a radius of 2 and a height of 10. Determine the volume.
125.6cm3
300
Find the IQR for the following data set:
101, 101, 127, 134, 155, 160, 177, 189, 190, 190, 195
Q1 = 127
Q3 = 190
IQR = Q3 - Q1
= 190 - 127
= 63
300
Calculate the standard deviation:
-12, -7, -5, -5, -1
1. Mean = (-12 + -7 + -5 + -5 + -1) / 5
= -6
S.d. = (-12 - (-6))^2 + ....
= 64 / 5
= sqrt (64/5)
= 3.58
300
Calculate the volume of the following cone:
h = 5cm, area = 12cm2
V = (1/3)Ah
= (1/3) x 12 x 5
= 20
300
Calculate the surface area of the pyramid below:
width/2 = 10/2 = 5cm
c2= a2 + b2
c = sqrt(122 + 52)
c = 13cm
Area of triangle = 1/2bh
= 1/2 x 10 x 13
= 65cm2
Area of square = s2
= 102
= 100
Surface area = area of square + (4 x area of triangle)
= 100 + (4 x 65)
= 360cm2
300
The following data set has a median of 6, determine the value of x.
1, 3, 4, x, 9, 12
x = 8
8 + 4 = 12
12/2 = 6
400
Calculate the volume of the following cone:
h = 10cm, r - 6cm
Volume = (1/3) x pi x r2 x h
=(1/3) x pi x 62 x 10
= 376.99cm3
400
Calculate the surface area of the cone below:
Area of circle = pi x r2
= pi x 32
= 28.274m2
Area of side = pi x r x h
= pi x 3 x 4
= 37.699m2
Surface area = 37.699 + 28.274 = 65.97
400
How do you determine the interquartile range?
IQR = Q3 - Q1
500
Calculate the volume of the following sphere:
V = (4/3) x pi x r3
= (4/3) x pi x 53
= 523.6cm3
500
Calculate the surface area of the sphere:
S.A = 4 pi r2
= 4 x pi x 42
= 201.06cm2