1. If the arithmetic mean of 7,9,11,13, x, 21 is 13,find the value of x. 2. The mean of 24 numbers is 35. If 3 is added to each number, what will be new mean.? 3. The mean of 20 numbers is 43. If 6 is substracted from each of the numbers,what will be new mean? 4. The mean of 15 numbers is 27. If each numbers is multiplied by 4,what will be new mean? 5. The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51kg, 45kg, 49kg, 46kg, and 44kg. Find the weight of the sixth boy. 6. The mean of the marks scored by 50 students was found to be 39. Later on it was found that a score of 43 was misread as 23. Find the correct mean. 7. The mean of 100 items was found to be 64. Later on it was found that two of the items were misread as26 and 9 instead of 36 and 90 respectively. Find the correct mean. 8. A cricketer has a mean score of 58 runs in 9 innings. Find out how many runs are to be scored by him in the tenth innings to raise the mean score to 61. 9. The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation. 10. A batsman in his 12th innings makes a score of 63 runs and thereby increase his average score by 2, what is his average after the 12th innings ? 11. The mean of 31 observations is 60. If the mean of the first 16 observations is 58 and that of the last 16 observations is 62, find the 16th observation.
12. The heights of 72 plants in a garden are given below : Heights(in cm) 58 60 62 64 66 68
No. of plants 12 14 20 13 8 5
Find the mean height per plant.
13. The mean of the following data is 21.6. find the value of p. X 6 12 18 24 30 36
F 5 4 p 6 4 6

14. The mean of the following data is 1.46. find the value of missing frequencies. No of accidents(x) 0 1 2 3 4 5...
...balances by branch. Does it appear that account balances are related to the branch?
Branch Smallest third Middle third Largest third 
Ohio 8 6 2 
Georgia 1 6 10 
Kentucky 5 5 4 
Pensylvania 6 3 4 
Ho: Account balances are independent of branch.
H1: Account balances are independent of branch
Test Statistic:
Chi square is given by (Oi – Ei)^2 / Ei ~ χ2 with 2*3= 6 degrees of freedom
The calculated value of chisquare is 11.89625
Critical value for 5% level of significance is 12.5916
Since the calculated value is less than critical value we accept null hypothesis and conclude that account balances are not related to the branch
g. Cite some examples and comment on your findings.
If we wish to know if any distinction is made in appointment on the basis of sex for the following data
 Employed Not Employed Total 
Male 1480 5720 7200 
Female 120...
...Random sample
It is often not necessary to survey the entire population.
Instead, you can select a random sample of people/or firms from the population and
survey just them.
You can then draw conclusions about how the entire population would respond based
on the responses from this randomly selected group of people.
This is exactly what political pollsters do  they ask a group of people a list of questions
and based on their results, they draw conclusions about the population as a whole with
those often heard disclaimers of "plus or minus 5%"
If your population consists of just a few hundred people, you might find that you need to
survey almost all of them in order to achieve the level of accuracy that you desire.
As the population size increases, the percentage of people needed to achieve a high
level of accuracy decreases rapidly.
In other words, to achieve the same level of accuracy:
Larger population = Smaller percentage of people surveyed
Smaller population = Larger percentage of people surveyed
Probability Sampling
A probability sampling method is any method of sampling that utilizes some form of
random selection.
In order to have a random selection method, you must set up some process or
procedure that assures that the different units in your population have equal
probabilities of being chosen.
Some basic terms
•
•
•
•
N  the number of cases in the sampling frame
n  the number of cases in the sample
NCn  the number...
...techniques.
Firstly we look at data analysis. This approach starts with data that are manipulated or processed
into information that is valuable to decision making. The processing and manipulation of raw
data into meaningful information are the heart of data analysis. Data analysis includes data
description, data inference, the search for relationships in data and dealing with uncertainty
which in turn includes measuring uncertainty and modelling uncertainty explicitly.
In addition to data analysis, other decision making techniques are discussed. These techniques
include decision analysis, project scheduling and network models.
Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as
descriptive statistics. It includes graphical and tabular summaries, as well as summary measures
such as means, medians and standard deviations.
Uncertainty is a key aspect of most business problems. To deal with uncertainty, we need a basic
understanding of probability. Chapter 2 covers basic rules of probability and in Chapter 3 we
discuss the important concept of probability distributions in some generality.
In Chapter 4 we discuss statistical inference (estimation), where the basic problem is to estimate
one or more characteristics of a population. Since it is too expensive to obtain the population
information, we instead select a sample from the population and then use the information in the
sample to infer the...
...
Contents
Question 1 3
Question 2a 5
Question 2b 6
Question 2c 7
Question 3a 8
Question 3b 8
Question 3c 10
Question 3d 11
Question 4 12
Question 5 14
References 15
Question 1
The sampling method that Mr. Kwok is using is Stratified Random Sampling Method. In this case study, Mr Kwok collected a random sample of 1000 flights and proportions of three routes in the sample. He divides them into different subgroups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary...
...Trajico, Maria Liticia D.
BSEd IIIA2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the nonstop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t like this...
...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between nonmoving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear,...
...
The case between Beauty and Stylish involves concept of a valid contract, precontractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a twosided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...
...1. A density curve consists of a straight line segment that begins at the origin (0, 0) and has
slope of 1.
a. Sketch this density curve. What are the coordinates of the right endpoint of the segment?
(Note that the right endpoint should be fixed so that the total area under the curve is 1.
This is required for a valid density curve.)
b. Determine the median, the first quartile (Q1), and the third quartile (Q3).
c. Relative to the median, where would you expect the mean of the distribution to lie?
Explain briefly.
The distribution is skewed left, so the mean will be left of the median.
d. What percent of the observations lie below 0.5? Above 1.5?
2. The following are the salaries of employees in a small business:
15,000 15,000 17,500 23,500 23,750 25,000 26,000 27,500 29,000 45,000
a. Before using your calculator, do you think that the mean or the median for these values
will be higher? Why do you think so?
b. What are the mean and median of the salaries? Was your answer to (a) correct?
c. Find the standard deviation and the IQR of the data
d. Describe the shape of the distribution terms of its overall shape, including outliers and
skewness. Be sure to give the locations of the main features
e. Speculate on the reasons for why the distribution is shaped as it is.
3. The following represents the outcomes of rolling a die 600 times (actually, it was
simulated on the TI83 as follows: RandInt (1,6,600)_L1).
Face
1
2
3 ...