Statistics Help Sheet
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Statistics Help Sheet
For these examples we will be using two different sets of numbers.
Set A:
Set B:
13, 10, 4, 12, 20, 14, 18
10, 23, 2, 7, 9, 15, 7, 20
When dealing with statistics it is often easier to put the data in order (smallest to largest).
4, 10, 12, 13, 14, 18, 20
2, 7, 7, 9, 10, 15, 20, 23
Mean (aka. Average):
To find the ’Mean’ of a set of numbers take the sum of all the numbers and divide it by the quantity of numbers.
4 + 10 + 12 + 13 + 14 + 18 + 20 = 91
2 + 7 + 7 + 9 + 10 + 15 + 20 + 23 = 93
91 ‚ 7 =
13
93 ‚ 8 =
11.6
Median:
The ’Median’ of a set of numbers is the value that is in the center. In set A, the median is 13.
4, 10, 12, 13, 14, 18, 20
2, 7, 7, 9, 10, 15, 20, 23
Since set B has no number in the middle the median is the average of the two center numbers (9 & 10).
Set B’s median is
9.5
(19 ‚ 2) .
Range:
The ‘Range’ of a set of numbers is the difference between the largest and smallest amount.
4, 10, 12, 13, 14, 18, 20
2, 7, 7, 9, 10, 15, 20, 23
20 - 4 =
16
23 - 2 =
21
Quartiles
To find the quartiles of a set, split the set into quarters (4ths). Set B’s quartiles are between numbers, so the average of the numbers is used.
4, 10, 12, 13, 14, 18, 20
2, 7, 7, 9, 10, 15, 20, 23
Q1:
10
Q1: 14 ‚ 2 =
7
Q2:
13
Q2: 19 ‚ 2 =
9.5
Q3:
18
Q3: 35 ‚ 2 =
17.5
Interquartile Range
The ‘Interquartile Range’ is the difference between the first quarter and the third quarter (see above).
4, 10, 12, 13, 14, 18, 20
2, 7, 7, 9, 10, 15, 20, 23
18 - 10 =
8
17.5 - 7 =
10.5
Mean Absolute Deviation
The ‘Mean Absolute Deviation’ is the mean of the numbers distance from the mean.
Number
Distance from Mean (13)
Number
Distance from Mean (11.6)
4
9
2
9.6
10
3
7
4.6
12
1
7
4.6
13
0
9
2.6
14
1
10
1.6
18
5
15
3.4
20
7
20
8.4
23
11.4
9 + 3 + 1 + 0 + 1 + 5 + 7 = 26
9.6 + 4.6 + 4.6 + 2.6 + 1.6 +3.4 + 8.4 +11.4 = 46.2
26 ‚ 7 =
3.7
46.2 ‚ 8 =
5.8
Math Help
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