Distribution Shapes
A distribution whose dot plot or histogram takes the form of a bell with most of the data clustered near the center and fewer points farther from the center
Bell-Shaped distribution
Find the median of the data set: 4, 8, 9, 1, 10
Median = 8
Simplify:
6m – 5m + 1
m + 1
3(2x - 9) = 3
x = 5
Solve for x
x/2=M-6
x=2(M-6)
A distribution where all of the data values have the same or very similar values.
Uniform Distribution
Find the mean of the data set: 4, 8, 9, 1, 10
Mean = 6.4
Simplify:
-6(4x - 5)
-24x + 30
3x + 4 + x + 2 = -30
x = -9
Solve for x
Ax+B=C
x = (C-B)/A
A distribution where one side of the distribution has more values farther from the bulk of the data than the other side, so that the mean is not equal to the median.
Skewed Distribution
Find the value of Q1 (lower quartile) and Q3 (upper quartile) of this data set:
0, 12, 4, 9, 10, 3 , 3
Q1 = 3
Q3 = 10
Simplify:
9 - 3(-6d + 9)
18d - 18
2 +9(x-1) = 2
x = 1
Solve for p
q+r=p/5
p=5(q+r)
A distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median.
Symmetric Distribution
Calculate the Interquartile Range of this data set:
15, 26, 12, 3, 19, 20, 6, 27
IQR = Q3 - Q1 = 14
Simplify:
-4(-5f - 3) +11 - 12f
8f + 23
x + 5 = 3 + x - 2
There are zero solutions to this equation.
"No solution"
Solve for a
z=9a-9-3b
a=(z+9+3b)/9
A distribution with two very common data values seen in a dot plot or histogram as distinct peaks
Bimodal distribution
Find the Mean Absolute Deviation (MAD) of the following data set:
44, 39, 18, 37, 32, 44
MAD = 7.111111
Simplify:
g - 4m + 2(m - 3) + 6 - 2g
-g - 2m
2(8x + 2) - 3(x + 10) = 3(4x + 1) - (-x + 29)
There are infinite solutions; x could be equal to any number.
Solve for a
u=(-2a-3)/(ka)
a=-3/(uk+2)