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Date:____________________________ Block:__________ Name:_________________________________
DESCRIPTIVE STATISTICS: organizing and describing data


A population is the set representing all measurements of interest.
A sample is a subset of measurements from the population.
MEASURES OF CENTRAL TENDENCY
When examining data it can be useful to know where the centre of the data lies.
Median: The piece of data in the middle when the
Mean: The arithmetic average
data is arranged in order
 calculated by adding all numbers and
dividing by how many there are
Example: The median of {3, 4, 4, 7, 8, 9, 10} is 7
Sum of all the data
because 7 is in the middle
Number of pieces of data
Example: The mean of 10, 14, 16, 16, 20 is
10  14  16  16  20
 15.2
5
Example: The median of {34, 40, 46, 48, 55, 60} is
47. The two numbers in the middle are 46 and 48,
and the mean of these two numbers is:
46  48
 47
2
MODE:
 the number that occurs most often
 can have more than one mode, or no mode at all
Example: The mode of {10, 11, 12, 12, 14, 14, 14, 17} is 14 since it occurs three times -- more than any
other number
Example: The mode of blue, blue, yellow, red, red, red, red, green, green is red since it occurs four times -more than any other color.
One of the advantages that mode has over the mean and median is that it is not restricted to numbers.
OUTLIERS: Values that are significantly different from the majority of a set of data
Example: {15, 14, 16, 15, 15, 16, 14, 15, 16, 17, 15, 14, 28}
Outlier is 28
Date:____________________________ Block:__________ Name:_________________________________
Do the following Question:
1. The marks (%) of a class quiz are shown:
82, 78, 69, 43, 56, 72, 73, 90, 100, 81, 68, 75, 86, 94, 55, 62, 79, 98, 57, 77
Calculate the mean and median of these marks. (Show all work.)
Mean:______________ Median:___________
GRAPHS
Histogram: shows bars that indicate the number of values
within a particular class or bin
Histogram
sample
10
9
8
Frequency Polygon: formed when the midpoints of the tops of
the bars on a histogram are joined by straight lines
Count
7
6
5
4
3
2
1
-10
-5
0
5
Attr9
10
15
20
Bin – the grouping of the data values; all bins must be the same width; there should be no more than 10 bins
(ideally 6 – 8 bins)
Frequency Table – a chart showing the grouping of the data values
Date:____________________________ Block:__________ Name:_________________________________
Example:
Create a frequency table and a histogram for the following ages of people at a school board meeting: 54, 32,
35, 27, 51, 56, 49, 51, 52, 44, 47, 38, 36, 61, 25, 51, 47, 30, 55, 45, 29, 50, 42, 36, 41, 29, 54, 52, 41, 39
Step 1: Create a frequency table
Step 2: Plot the data (Add a title and a legend)
Age of People Attending School Board Meeting
Bin
20-30
30-40
40-50
50-60
60-70
Frequency
1111 →4
1111111→ 7
11111111 →8
111111111→ 9
1→1
10
frequency
9
8
7
6
5
4
3
2
1
age (years)
10
20
30
40
50
60
70
80
90 100
Do the following Questions:
4.
Fingerprints can be classified according to the number of ridges between “loops” in the patterns. The
number of ridges is called the ridge count for a particular person. A histogram was constructed based
on the data collected from randomly selected adults.
frequency
ridgecount
a) How many bins are there? _____
b) How many people participated in the data collection?____
c) How many people had ridge counts less than 195?_____ What is this as a percent?_____
d)
How many people had ridge counts between 190 and 205?____ What is this as a percent?__
Date:____________________________ Block:__________ Name:_________________________________
1. Following is a table of masses in kilograms for 50 grade 10 students.


48
61
55
56
52
58
59
55
54
55
54
58
56
56
51
48
51
60
55
56
54
57
53
49
57
51
56
51
55
53
Fill out the frequency table below (tally is
optional)
Construct a histogram
BIN
Width
48 – 50
Tally
55
54
53
54
53
52
56
59
50
55
57
52
57
50
56
51
54
53
58
53
Frequency
50 – 52
52 – 54
54 – 56
56 – 58
58 – 60
60 – 62
MEASURES OF DISPERSION
When examining data it can be useful to know whether the numbers are widely spread out, or whether they
are clustered around the mean. Two common ways to measure what the dispersion are range and standard
deviation.
Range: The difference between the smallest and largest data values.
Standard Deviation: The deviations (or distance) from the mean; if the standard deviation is small, the
data are close to the mean; if it is larger, the data are more spread out.
Standard Deviation formula:
 x  x 
2

n
:
standard deviation
x : data value
x : mean
n : number of data values
Step 1: Find the mean of the data.
65  83  72  79  96 395

 79
Mean =
5
5
Step 2: Subtract the mean from each data value.
Step 3: Square this value.
Step 4: Find the mean of all the values squared.
Step 5: Take the square root of the mean. This is
your standard deviation.
Date:____________________________ Block:__________ Name:_________________________________
Example:
Find the standard deviation of the following grades: 65, 83, 72, 79, 79, 96
x
 Mean of ( x  x ) 2 values :
x
xx
( x  x) 2
550
79
65
79-65 = 14
(14)2 = 196
 110
2
5
79
83
79-83 = -4
(-4) = 16
 Take the square root of this value.
79
72
79-72 = 7
(7)2 = 49
2
This is your standard deviation.
79
79
79-79 = 0
(0) = 0
2
79
96
79-96 = -17
(-17) = 289
110  10.48
Do the following Question:
2. The time, in seconds, that it takes 10 runners to run an 800-metre race are:
114 116 116 119 120 120 121 121 125 128
a) Find the mean time.
b) Calculate standard deviation. Show your work.
HW: Please read ch 20A pg 500 and Do pg 505 #3,4
Please read ch 20B pg 505 -509 and Do pg 1,4,10