Download f7ch1 - Pui Ying Secondary School

1.1 Populations and Samples
(1)
Population Parameters and Sample Statistics Population
(2)
Simple Random Sampling
(3)
Population Size
(1) Population Parameters and
Sample Statistics Population
(2) Simple Random Sampling
 “RAN#” key
 construct a random number table
Answer (for reference)
0.871 0.843
 0.583 0.201
 0.532 0.932
 0.561 0.119

0.874
0.199
0.508
0.206
0.237
0.565
0.710
0.364
0.451
0.298
0.900
0.814
0.770
0.830
0.661
0.366
0.962
0.727
0.481
0.964
0.980
0.690
0.484
0.703
(3) *Population Size
 N is larger than or equal to 10.
 *[Notice: Size of a population need not be large. ]
1.2 Central Tendency
1. mean
2. median
3. mode
1. mean






Population Mean for Ungrouped Data
Sample Mean for Ungrouped Data
Population Mean for Grouped Data
Sample Mean for Grouped Data
Combined Sample Mean
The Weighted Mean
2. median

Median of data arranged in order of magnitude

The median =

Median Found by Ungrouped Frequency Distribution
Median Found by Grouped Frequency Distribution

 x N 1
 2
1
 ( x N  x N 1 )
2
2 2
if N is odd .
if N is even.
(i) Median Found by Ungrouped
Frequency Distribution
(ii) Median Found by Grouped
Frequency Distribution
3.mode
 In general, the mode of a set of data is the
value which occurs most frequently in the
set.
1.3 Measures of Dispersion
(Dispersion and Varibility)
1. The Range
2. The Interquartile Range, the Five-
number summary and box plots
3. The Variance and the Standard
Deviation
1.The Range
 The range of a set of data is the difference between the






largest value and the smallest value of the set.
Example 1
Find the ranges of the following sets of data:
A = {40, 41, 42, 58,59,60}
B = {20,20.1,20.2,59.1,59.2,60}
C = {10,20,30,40,50,60,70}
The range of A =
The range of B =
 The range of C =
2.The Interquartile Range, the Fivenumber summary and box plots
Lower Quartile
 Median
 Upper Quartile



Q1
Q2
Q3
The Interquartile Range
1
(n  1)th
4
1
(n  1)th
2
3
(n  1)th
4
value
value
value
= Upper Quartile – Lower Quartile
= Q3- Q1
Example 6
 Find the interquartile range of the following
set of numbers.
2,3,3,9,6,6,12,11,8,2,3,5,7,5,4,4,5,12,9
Example 7

The table gives the cumulative distribution of the
heights (in cm) of 400 children in a certain school:
Height(cm)
Cumulative
Frequency
<100
<110
<120
<130
<140
<150
<160
<170
0
27
85
215
320
370
395
400
Find
(i)Draw a cumulative frequency curve.
(ii)Estimate the median.
(iii)Determine the interquartile range.
The Five-number summary and
box plots
 The format of Box and Whiskers diagram is
shown below:
x
Minimum
Q1
Q2
Q3
Maximum
C.W. Q3


The weekly expenditure on soft drinks of 20 football players re given in
the following table:
Expenditure on soft drinks of 20 football players(in dollars)
26
34
31
36
16
27
32
21
43
41
30
6
15
38
27
58
35
28
21
20
Find
 Maximum value =
 Upper quartile =
 Median =
 Lower quartile =
 Minimum value =
 and then draw the Box and Whiskers diagram
3.The Variance and the Standard
Deviation

(I)Population variance and
population standard deviation

(II)Sample Variance and Sample
Standard Deviation
(I) Population variance and
population standard deviation
 Population variance, 2 =
N
 (x
i 1
i
 )
2
N
 Population Standard Deviation,  =
N
 (x
i 1
i
 )
N
2
(II) Sample Variance and Sample
Standard Deviation
 Sample Variance s2
1 n
2
(
x

x
)

i
n  1 i 1
Example 1
 Two machines, A and B, are used to pack biscuits. A
sample of 10 packets was taken from each machine and
the mass of each packet, measured to the nearest gram,
was noted.
Machine A(mass in g)
196,198,198,199,200,200,201,201,202,205
Machine B(mass in g)
192, 194, 195, 198, 200, 201, 203, 204, 206, 207
(i) Find the standard deviation of the masses of the
packets taken in the sample for each machine.
(ii)Comment on your answer.
C.W.
mean ,standard deviation
 The following are two sets of data of an experiment
obtained by two different students:
Volume of acid measured (cm3)
 Student A
8,12,7,9,3,10,12,11,12,14
Student B
7,6,7,15,12,11,9,9,13,11
(i) What is the mean volume of acid measured by each
student?
(ii) What is the standard deviation?
(iii) Which set of results is more reliable?