Download MHF Unit 16 Sections 16AB Notes

Unit 16: Statistics
Sections 16AB Central
Tendency/Measures of Spread
Example 1:The following figures
represent the average marks of some the
grade 12 students applying to university
next year.
75, 72, 76, 63, 64, 66, 70, 82, 76, 70
The data can be analyzed using measures of
“Central Tendency”.
They are the mean, median, and mode
The mode is the data item or the class of data that occurs
most often.
It is possible for there to be more than one mode
(bimodal, trimodal etc.).
If all the data values or classes occur only once, then
there is no mode.
If we arrange our data we have
63, 64, 66, 70, 70, 72, 75, 76, 76, 82
The modes are 70 and 76 (bimodal)
The median is found by arranging all the data in order from
least to greatest and selecting the middle item.
If there are an even number of data items, then there are
two middle items.
The median is the mean of these two items.
63, 64, 66, 70, 70, 72, 75, 76, 76, 82
The median for our data is
71
The mean is the measure of central tendency that is used
most often. It is found by adding the numeric data and the
result is divided by the number of data items.
If an entire POPULATION is known, then we can
calculate the mean of the population “”
If we only have a SAMPLE of the population, then
we calculate the mean of the sample “”
If a set of data has outcomes x1, x2, …xn, then
Mean
x

x
i
n
714
x
 71.4
10
Many of these statistics can be
determined using your calculator
Measures of spread or variability is another
way to compare data
Percentile Ranking: If a student is in the 75th percentile, it
means that the student finished higher than 75% of all the
other students
For example, if scores on a test were as follows:
63, 64, 66, 70, 70, 72, 75, 76, 76, 82
To calculate the 75th percentile
75% of 10 scores = 7.5 scores
The 75th percentile is the 8th score from the bottom
Therefore the 75th percentile score is 76
Quartiles
When data is arranged in order from least to greatest, the
median is the middle number in the set of data.
Quartiles represent the data items that are one quarter and
three quarters of the way through a set of data
For example, consider the set of data
63, 64, 66, 70, 70, 72, 75, 76, 76, 82
Lower quartile Q1
Median
Upper quartile Q3
66
71
76
Interquartile range
Q3-Q1=76-66=10
Variance
The average of the squares of the deviation from the mean is
called the Variance.
1
   ( xi  x ) 2
n
2
This is a difficult formula to use
So we can rearrange it to give.
1
2
   xi  x 2
n
2
Standard Deviation
The Standard Deviation is the square root of the
variance. It represents the
“Average distance from the Mean”

1
2
2
x

x

i
n
If we refer back to our calculator
HOMEWORK:
PAGE 468 # 1, 2, 4 – 8
Correction#2a
mean = 19.5, med = 15, mode = 15
PAGE 471 # 1 – 5
Do 16A#1 and 16B # 1 together