Methods for Summarising Sample Data 5Nov09

1
Methods for Summarising Sample Data 5-Nov-09

• Objectives
• You should understand and know how to find or
  calculate the
• Mode and modal class
• Median, lower and upper quartiles and show these
  on a box plot
• The true, sampler and estimated mean
• Use coding to simplify data

2
Mode The number or thing that there is the most
frequent. What is the MODE of 2, 7, 2 , 1 and 8
? Mode 2 What is the MODAL colour of these
beads? Modal Colour Red
Modal Class is 3 - 5
3
Median The middle value in a set of
numbers What is the MEDIAN of 2, 7, 2, 1 and
8? Put the numbers into rank order and then find
the middle value. 1, 2, 2, 7, 8 Median 2 What
is the median of 2, 7, 3, 1, 8 and 7?
1, 2, 3, 7, 7, 8 Median 5
If you get two numbers in the middle add these
together and then divide by 2
4
Find the Median for Grouped Data First find the
class that contains the median (150 1) 2
75.5 It is between the 75th and 76th Now use the
formula m b (½n f) fm x w b lower
class boundary n sum of all the freq. f sum
of frequencies below b fm frequency of the
median class w width of the median class
Add one to the total frequencies and then divide
by 2
Median 4.5 (½ x 150 32) 71 x 5 Median
4.5 3.03 ? Median 7.5 visits
5
Find the Lower Quartile First find the class
that contains the lower quartile (150) 4
37.5 It is between the 37th and 38th Now use
the formula lq b (¼n f) fm x w b
lower class boundary n sum of all the freq. f
sum of frequencies below b fm freq. of the
quartile class w width of the quartile class
LQ. 4.5 (¼ x 150 32) 71 x 5 LQ. 4.5
0.38 ? LQ. 4.38 visits
6
Find the Upper Quartile First find the class
that contains the upper quartile (150) X 0.75
112.5 It is between the 112th and 113th Now use
the formula uq b (¾n f) fm x w b
lower class boundary n sum of all the freq. f
sum of frequencies below b fm freq. of the
quartile class w width of the quartile class
UQ. 9.5 (¾ x 150 103) 20 x 5 UQ. 9.5
2.38 ? UQ. 11.88 visits
7
Find a Percentile eg 95 First find the class
that contains the percentile (150) X 0.95
142.5 It is between the 142nd and 143rd Now
use the formula b (0.95n f) fm x w b
lower class boundary n sum of all the freq. f
sum of frequencies below b fm freq. of the
percentile class w width of the percentile class
There are only 5 of the patients that require
more the 22 visits.
P95 19.5 (0.95 x 150 137) 10 x 5 P95
19.5 2.75 ? P95 22.25 visits
8
Box and Whisker Plot
A set data has a smallest value of10 and a
largest value of 80. The median is 37and LQ is
20 and the UQ is 60.
LQ ? Q1 Median ? Q2 UQ ? Q3
9
Here are the ages of ten people 2, 11, 12, 12,
17, 18, 21, 23, 24 and 30 What is the mean?
Total the numbers ? 170 Divide by the number of
numbers 170 10 17 The mean is 17
This is the true mean
10
Here are the ages of ten people 2, 11, 12, 12,
17, 18, 21, 23, 24 and 30 What is the sampler
mean?
Take a random sample
A sample of the ages is 11, 17, 18 1nd 24 Total
and divide by the number of terms in the
sample 70 4 17.5 The sampler mean is 17
This is the sampler mean and will vary depending
upon the choice of the sample
11
2, 11, 12, 12, 17, 18, 21, 23, 24 and 30
The ages are put into a frequency table. This is
convenient put the unique values are lost.
What is the estimated mean?
12
(No Transcript)
13
Estimated Mean ?fX ?f
? 176 10 17.6
14
Coding
Find the mean of 1020, 1120, 1200 and 1100 Mean
4440 4 ? Mean 1110 The data can be coded by
the operations Minus 1000 and then divide by
10 Coded data 2, 12, 20 and 10 Coded Mean 44
4 ? Coded Mean 11 The coded mean is then
decoded by Multiply by 10 and then plus 1000 11 ?
11 x 10 110 ? 110 1000 1110