What is the sample size denoted by?
Click to see answer
n (n = 5).
Click to see question
What is the sample size denoted by?
n (n = 5).
How is each element in the sampling frame identified?
By giving each element a unique identity number.
Can two data sets with the same mean have different spreads?
Yes, they can have completely different spreads.
What should be done with numbers outside the range of 0001 to 3000?
They must be discarded.
Why is it impractical to prepare a sampling frame for the example provided?
Because the population size is very large, all teenagers in Hong Kong.
In the provided example with a sample size of 15, what is the mode?
There is no mode as all data have the same frequency.
What is the population size in the example regarding the cola brand survey?
All teenagers in Hong Kong.
What does a census involve in the context of employee satisfaction?
Collecting data from every employee in the company.
What is a convenience sample?
A sample selected based on ease of access, such as street interviews.
What is a disadvantage of Simple Random Sampling?
It can be time-consuming for large-scale surveys.
What is Q1 in the provided example?
Q1 = 420 items (25th percentile).
What is the mode in a data set?
The value that occurs most frequently.
What is one of the key topics covered in the Elementary Statistics course?
Probability Distributions.
What does the positive square root of the variance represent?
The standard deviation of X.
What is crucial for the reliability of conclusions drawn from a survey?
How representative the sample is of the population.
What is Q3 in the provided example?
Q3 = 890 items (75th percentile).
What characterizes a symmetric distribution?
In a symmetric distribution, the parts above and below its center are mirror images in the density function.
What indicates a right-skewed distribution?
A right-skewed distribution has a longer right side.
Is the interquartile range affected by extreme values?
No, it is not affected by extreme values.
What indicates a left-skewed distribution?
A left-skewed distribution has a longer left side.
How do you clear previous data on the Casio fx-50FH calculator?
Press SHIFT, then CLR, select Stat, and press EXE.
What is the sample mean?
The average result calculated from a subset of the population, which can vary depending on the selected data.
How is standard deviation related to variance?
Standard deviation is the square root of the variance.
What are the characteristics of a numerical random variable?
Its value is uncertain and unpredictable, and it can be presented as a numerical value.
Why is summarizing a discrete variable as a probability distribution function useful?
It helps understand the possible range of outcomes and evaluate which outcomes have higher chances of occurring.
What are the three major types of descriptive measures in statistics?
Central tendency, variation, and shape.
What is the interquartile range (IQR)?
The difference between the third quartile (Q3) and the first quartile (Q1) in a set of data.
What is the significance of the course in relation to further studies?
It cultivates interest in quantitative techniques necessary for further studies.
What is the sample standard deviation (𝑠) calculated in the example?
229.54 items.
What statistical analyses might be performed after data collection?
Calculation of mean and standard deviation of the scores.
How are individual samples selected in stratified sampling?
Randomly from each of the strata.
What is the formula for population variance?
σ² = (1/N) * Σ(x - μ)²
What is the formula for variance of Y?
Var(Y) = Σ [f(xi)² * p(xi)] - E(Y)².
What are some methods to collect a representative sample?
Simple random sampling, systematic sampling, and stratified sampling.
What is the expected value E(X) of the weekly sales of 'PhotoC'?
2.15 items.
What is empirical probability?
Probability based on observed frequencies from experiments.
What is the empirical probability of observing a 1 when tossing an unfair die?
P(1) = 0.1.
What is the probability of 10 tourists visiting Ocean Park?
0.006.
What is a key analysis method for a normal variable?
Analyzing a function of a normal variable.
What should you check frequently for updated course information?
SOUL course link and class link.
Why might the average number of books borrowed (4.35) not reflect individual borrowing behavior?
Because not every reader borrows the same amount, and it's not possible to borrow a fractional number of books.
What should you do if the index i is not an integer?
Round up i to the nearest integer.
What is Simple Random Sampling?
A method that selects objects such that every object of the population has an equal chance of being selected.
What does the notation P(X = x) represent?
The probability that the random variable X takes on the value x.
What type of assessment is included in the course?
Individual assignments and a final examination, each worth 50 marks.
What is the numerical random variable for a tour guide managing tourists?
The number of tourists that may go to Ocean Park.
What is stratified sampling?
A method that divides the whole population into subgroups (strata) based on a common characteristic.
What is systematic sampling?
A method that selects the first object randomly and the rest by a fixed interval k.
What do variance and standard deviation evaluate?
How the values fluctuate about the mean.
Define an event in probability.
Each possible type of occurrence in a sample space.
How can we determine the probability distribution function for an unfair die?
By conducting experiments and calculating empirical probabilities based on observed relative frequencies.
What is the probability distribution function based on the observed frequencies from the die toss?
1: 0.18, 2: 0.12, 3: 0.32, 4: 0.16, 5: 0.12, 6: 0.10.
What is an example of a right-skewed distribution?
Monthly income of fresh graduates.
What are the two types of variables in statistics?
Numerical variable and categorical variable.
What is a sampling frame?
A data file that contains information of the population objects.
What type of calculator is required for the course?
An HKEA approved calculator with SD (statistics) function.
What is a continuous numerical variable?
Data that covers a range of values.
What is the probability distribution function p(x) for the number of books borrowed?
P(X=x) = {0.02, 0.07, 0.15, 0.28, 0.33, 0.10, 0.03, 0.02} for x = {1, 2, 3, 4, 5, 6, 7, 8}.
How is the mode different from other measures of central tendency?
The mode is not affected by extreme values.
How many employees are in the company mentioned in the study?
3000 employees.
In the context of a librarian, what is a numerical random variable?
The number of books the next reader may borrow.
Why might a survey be conducted instead of a census?
Due to limitations like time and budget.
What is the significance of standard deviation in relation to the mean?
It indicates the average difference of the data from the mean.
In the example provided, what is the sample size and total population?
Sample size is 500 and total population is 3000 employees.
In the example provided, how many managers were selected for the stratified sample?
100 managers.
What are the two methods to prepare the probability distribution function?
Method 1: Use past records of tourists visiting Ocean Park. Method 2: Use a theoretical Binomial distribution based on a 60% visit rate.
What is a key characteristic of the mean?
It is affected by extreme values.
How can skewness be identified using quartiles?
By comparing Q1, Q2, and Q3: symmetric if Q2 - Q1 = Q3 - Q2, left-skewed if Q2 - Q1 > Q3 - Q2, and right-skewed if Q2 - Q1 < Q3 - Q2.
What does it indicate if Q2 - Q1 > Q3 - Q2?
The distribution is left skewed.
What can be calculated for a function of a variable?
Expected value, variance, and standard deviation.
How do you calculate the mean on the Casio fx-50FH calculator?
Press SHIFT, then 2, then 1, and then EXE.
What is the mean result of Class 1 in the example?
75.3 marks.
What is the mean result of Class 2 in the example?
81.4 marks.
What is the mean result of Class 3 in the example?
74.2 marks.
What is a discrete numerical variable?
Data that only takes place at particular values, usually integers.
What is the expected value of Y if E(X) = 2.15?
E(Y) = -3500 + 4340(2.15) = $5831.
What is the relationship between the mean of Y and the mean of X in a linear function?
Mean(Y) = a + b * Mean(X)
What is the 10th percentile in the given example?
345 items.
What type of variable is the number of previous full-time employment?
Discrete numerical variable.
What is a probability distribution function for a discrete random variable?
A mutually exclusive listing of all possible numerical outcomes with associated probabilities.
What are the properties of a probability distribution function?
What is the range of scores employees can give regarding their satisfaction?
From 0 to 10.
How is the interquartile range calculated?
IQR = Q3 – Q1.
What is skewness in data distribution?
Skewness refers to the asymmetry of the distribution of data values.
What is the standard deviation of the number of books borrowed from the library?
1.3444 books.
What does a mean satisfaction score of 2.4 indicate?
A very low level of satisfaction.
What is the basic workflow of conducting a survey?
It involves planning, collecting data, and summarizing findings.
What is the sample size for junior staff in the example?
400 junior staff.
What is the probability that 4 to 8 tourists will visit Ocean Park?
The probability is 0.899.
What is the 75th percentile (Q3) in the example?
890 items.
What does a small variance indicate?
The data points are located closely together.
How is the population mean calculated in the example provided?
By averaging the examination results of all year 1 students, resulting in a mean of 78.65 marks.
What is the standard deviation σ(X) of the weekly sales of 'PhotoC'?
1.0618 items.
What is the probability of 0 tourists visiting Ocean Park?
0.0001.
What is the formula for the standard deviation of Y when Y is a linear function of X?
σ(Y) = |b|σ(X).
Given Y = 4340X - 3500, what are the values of a and b?
a = -3500, b = 4340.
What is the p-th percentile?
The maximum value that (about) p% of the observations are smaller than.
How is the index i calculated for finding the p-th percentile?
i = n * (p/100), where n is the number of data points.
What does the 50th percentile represent?
The second quartile (Q2), which is the median.
What type of variable is total working hours on 1/9/2019?
Continuous numerical variable.
How is collected data typically denoted?
With a small letter (e.g., x).
When is a convenience sampling method practical?
When no sampling frame is available.
What tool can be used for Simple Random Sampling?
A Random Number Table.
What is the variance of a random variable X denoted as?
σ² or Var(X).
What is the range of the data set: 300, 345, 368, 420, 488, 522, 627, 668, 731, 774, 802, 890, 902, 904, 990?
Range = 990 – 300 = 690.
What numerical random variable is analyzed by a researcher in telecommunications?
The duration of long-distance calls.
How can using computer software improve the sampling process?
It can generate random numbers much faster while maintaining the same underlying logic.
How is the fixed interval k calculated in systematic sampling?
k = total population size / sample size.
What is the sample size (n) in the example?
What does the interquartile range measure?
The spread of the middle 50% of the data.
What does X represent in the example provided?
The number of photocopiers sold in a week.
What happens when you multiply the mean by the number of data points?
It equals the total value.
What is a disadvantage of stratified sampling?
It is more complicated.
What is the command to input data into the Casio fx-50FH calculator?
Input each data point followed by pressing DT.
What is a disadvantage of systematic sampling?
The sample may be biased when studying periodic data.
What is the expectation (or expected value) of a discrete random variable X?
It is the weighted average over all possible outcomes, with weights being the probabilities associated with each outcome.
What was the range of items sold?
690 items.
What percentage of salespersons sold less than 345 items?
The bottom 10%.
Given the probability distribution for the number of books borrowed, what is E(X)?
E(X) = 4.35 books.
Are calculators with graphical displays allowed in the examination?
No, they will not be allowed.
What will be explored in Chapter 4 regarding sample means?
Using a randomly selected sample mean to estimate the population mean with high accuracy.
In the provided survey example, what type of variable is 'Number of previous full-time employment'?
Numerical variable (Discrete).
What scale is gender measured on?
Nominal scale.
What is the primary focus of the Elementary Statistics course?
Teaching quantitative skills applicable to daily life problems.
What is the first step in the sampling process for selecting employees?
Assign unique identity numbers to each employee from 0001 to 3000.
What happens if the same number is selected more than once?
It must also be discarded.
What is the notation for population mean?
μ (mu).
What are strata in stratified sampling?
Subgroups that are mutually exclusive and exhaustive.
How can distributions be classified based on skewness?
Distributions can be classified as symmetric, left-skewed, or right-skewed.
What is the interquartile range (IQR) for the given data?
IQR = 890 – 420 = 470 items.
What is the expected value of weekly profit (E(Y))?
$5831.
What is a function of a random variable?
A function Y = f(X) where Y is studied based on the random variable X.
What is the focus of Chapter 2 in Elementary Statistics?
Methods to describe characteristics of a numerical random variable.
What is the 50th percentile (Q2) in the example?
668 items.
What is the 90th percentile of the monthly salary?
$47,120.
What is a population in statistics?
The totality of elements (items, objects) under consideration.
What is the range of the monthly salary?
$20,700.
What is an advantage of systematic sampling?
It is time-saving.
What distribution is used to derive the probability distribution function in this example?
Binomial distribution.
What is the command to calculate the population standard deviation?
Press SHIFT, then 2, then 2, and then EXE.
Why should probability samples be used?
To minimize the possible chance of getting biased results.
What does a numerical variable consist of?
Data that consists of numbers representing counts or measurements.
Why is the sample mean not unique?
Its value depends on which data are selected in the sample.
What is the final step to return to normal mode on the Casio fx-50FH calculator?
Press MODE and then 1.
What is the first step in finding the p-th percentile?
Arrange data in an ordered array.
In the provided survey example, what type of variable is 'Total working hours on 1/9/2019'?
Numerical variable (Continuous).
How is a variable typically denoted?
With a capital letter (e.g., X).
What is the example given for selecting a sample of teenagers?
Inviting 500 teenagers to join a survey about a cola brand.
What does variation measure in a data set?
The amount of dispersion or spread in the data.
What does a mean satisfaction score of 9.5 indicate?
A very high level of satisfaction.
What is the notation for sample mean?
𝑥̅ (x-bar).
How is the expected weekly profit calculated?
By substituting values of X into the profit function and using the probability distribution.
What does the mean represent in a data set?
It shares the total by the number of data equally.
What is the 10th percentile of the monthly salary?
$30,350.
What is the formula for sample variance?
s² = (1/(n-1)) * Σ(x - x̄)²
What is the difference between a census and a sample survey?
A census collects data from every member of a population, while a sample survey collects data from a subset.
Why is understanding the probability distribution of a variable important?
It provides insight to predict outcomes under uncertain situations.
What is the population mean?
The average result of all individuals in a population, reflecting its characteristics, calculated when a census is conducted.
What is the classical probability of observing a 1 when tossing a fair die?
P(1) = 1/6.
What is a census?
Investigation based on the data of the whole population.
What is an example of a left-skewed distribution?
Examination results.
What is the objective of the survey conducted by the manager?
To understand the employees' satisfaction level towards the company.
What scale is used to measure employee satisfaction?
A 10-point scale ranging from 0 (very unsatisfied) to 10 (very satisfied).
What is the most ideal method for conducting the survey?
Conducting a census of all 3000 employees.
What summary statistics might be used in the survey results?
Mean, standard deviation, 25th percentile, and 75th percentile.
What does the variance measure in the context of a discrete random variable?
It measures the dispersion of the variable.
How is the monthly salary calculated if the basic salary is 30 for each item sold?
Y = 20000 + 30X
What is the formula for the range of Y in terms of the range of X?
Range(Y) = |b| * Range(X)
What should students be able to do upon completion of the Elementary Statistics course?
Apply fundamental statistical skills in practice and analyze and present data using basic statistical methods.
Can the mode be used in categorical data sets?
Yes, the mode can also be used in categorical data sets.
What is an example of a numerical random variable when tossing a die?
The side that may face up.
How is the variance of X defined?
As the weighted average of the squared discrepancies between each possible outcome and its mean.
What is an advantage of Simple Random Sampling?
It is easy to operate.
What affects the range of a data set?
Extreme values.
What do measures of central tendency and variation together provide?
A good picture of a data set.
What is the formula for calculating the sample mean?
𝑥̅ = (Σ𝑥) / n.
What is the average number of books a reader borrows from the public library?
4.35 books.
What is the variable Y in the example?
The number of tourists, out of a group of 10, who will go to Ocean Park.
What is the variance of weekly profit (Var(Y))?
21237139 ($²).
How do you select the first subject in systematic sampling?
Randomly from the first k employees using a random number table.
What are the key components used to summarize a numerical discrete variable?
Probability distribution function, expected value, variance, and standard deviation.
What is the probability distribution function for the number of 'PhotoC' sold?
x: 0, 1, 2, 3, 4, 5; p(x): 0.05, 0.22, 0.38, 0.24, 0.10, 0.01.
What was the average number of items sold by a salesperson?
648.73 items.
What is the variance Var(X) of the weekly sales of 'PhotoC'?
1.1275 (items^2).
What percentage of individual tourists are expected to visit Ocean Park based on previous experience?
60%.
How is the variance of Y calculated when Y is a linear function of X?
Var(Y) = b²Var(X).
What percentage of salespersons sold more than 904 items?
The top 10%.
What are examples of a sampling frame?
Telephone directory, student registration list, employment record.
What is the variance of Y if Var(X) = 1.1275?
Var(Y) = 4340²Var(X) = 21237139 ($²).
How can the percentile of Y be expressed in terms of the percentile of X?
Percentile pth (Y) = a + b * Percentile pth (X)
What does the 75th percentile represent?
The third quartile (Q3).
What are the categories used for gender?
'M' and 'F'.
What theorem is included in the course topics?
Central Limit Theorem.
What is the sample size (n) in the example?
What is the formula for variance Var(X)?
Var(X) = E(X²) - E(X)².
What defines discrete data?
Data that only takes place at particular values.
Why is the sample variance calculated using n - 1?
To make it the best estimator of the population variance.
How is the sample mean calculated from the sales data example?
Sample mean = 648.73 items.
What is a sample space?
The collection of all possible events in an experiment.
What is the standard deviation of weekly profit (σ(Y))?
$4608.38.
What is the probability of observing an odd number when tossing a fair die?
P(odd) = 3/6 = 1/2.
How can sample standard deviation be calculated besides using the formula?
By inputting the dataset into a calculator.
What are the two main types of survey sampling methods?
Probability samples and non-probability samples.
How can you change a data point on the Casio fx-50FH calculator?
Use ▲/▼ until you see the data point, then input the new value and press EXE.
What is the process to delete a data point on the Casio fx-50FH calculator?
Use ▲/▼ until you see the data point, then press SHIFT and DT.
What is the general form of a simple linear function?
Y = a + bX
What is a nominal categorical variable?
A variable with no natural order between categories.
What is the relationship between the standard deviation of Y and the standard deviation of X?
SD(Y) = |b| * SD(X)
What are the categories for highest education level in order?
'Undergraduate', 'HKALE graduate', 'HKCEE graduate'.
What is the range in a data set?
The difference between the largest and smallest observations.
What are some methods to prepare a probability distribution function?
Theoretical approach, experiment, observation, survey, etc.
What is the sample mean (𝑥̅) calculated in the example?
648.7333 items.
What is the formula for calculating the population mean?
μ = (Σ𝑥) / N.
What defines continuous data?
Data that covers a range of values.
What was the mean monthly salary of the salesperson?
$39,461.90.
What is the 25th percentile (Q1) in the example?
420 items.
What is the median monthly salary of the salesperson?
$40,040.
What is the first step to use the Casio fx-50FH calculator for descriptive statistics?
Change to 'SD' mode by pressing MODE twice and then SD.
What is one advantage of stratified sampling?
It can avoid unbalanced selection.
What is the standard deviation of the monthly salary?
$6,886.20.
How many combinations are there when selecting 3 students from 10?
10 C 3 = 120 possible combinations.
What is the purpose of reading the probability density function?
To analyze a numerical continuous variable.
What can be calculated for a normal variable?
The probability function.
What does locating the normal score of a normal variable involve?
Identifying the position of a value within a normal distribution.
What is the probability of getting a 1 on the first toss and a 6 on the second toss of an unfair die?
P(first 1 and the second 6) = 0.0242.
What will be discussed in Chapter 3 regarding sample means?
The relationship between random sample means and the population mean.
How should the number 23.56474 be corrected to 4 decimal places?
23.5647.
In the provided survey example, what type of variable is 'Gender'?
Categorical variable (Nominal).
How is the variance of Y calculated in terms of the variance of X?
Variance(Y) = b² * Variance(X)
What type of variable is the highest education level?
Categorical variable.
How is the range calculated?
Range = Maximum data – Minimum data.
What is one of the topics related to data analysis covered in the course?
Estimation.
What is the sample variance (𝑠²) calculated in the example?
52690.50 items².
What is the variance of the number of books borrowed from the library?
1.8075.
What is the formula for calculating the monthly salary of a salesperson?
Y = 20000 + 30X, where X is the number of items sold.
Why is standard deviation more commonly used than variance?
Because it is in the original units of the data.
What is the first step in the systematic sampling process?
Assign unique identity numbers to each employee.
What is the probability distribution function for a fair die?
Each outcome (1 to 6) has a probability of 1/6.
What is the target average weekly profit for the photocopier 'PhotoC'?
$5000.
What is the helpful financial formula for profit?
Profit = Revenue - Cost.
What is an example of a symmetric distribution?
The height of a 10-year-old boy.
How can a numerical dataset be presented?
Using mean, mode, percentile, range, inter-quartile range, variance, standard deviation, and skewness.
What is the variance of the monthly salary?
47419749.00 ().
What is the formula for the expected value of Y when Y is a linear function of X?
E(Y) = a + bE(X), where Y = a + bX.
What are the basic expenses contributed to selling 'PhotoC'?
$3500.
What is the selling price of each 'PhotoC'?
$5340.
What is the median number of items sold?
668 items.
What does a categorical variable consist of?
Data that consists of names representing categories.
What is an ordinal categorical variable?
A variable where there exists a natural order between categories.
What does the 25th percentile represent?
The first quartile (Q1).
What scale is the highest education level measured on?
Ordinal scale.
What is the function that represents weekly profit in terms of sales?
Y = f(X) = 4340X - 3500.
What is the major idea behind stratified sampling?
To ensure the same proportion of representatives in each of the strata.
What is probability?
The likelihood or chance that a particular event will occur.
What does the variance represent in terms of units?
Squared units of the original data, e.g., squared dollars.
What is the calculated value of k in the example?
k = 6.
What does (x - μ)² measure?
The square difference of the data point to the mean.
What is the probability of exactly 5 tourists visiting Ocean Park?
0.201.
What is the difference between numerical and categorical variables?
Numerical variables represent measurable quantities, while categorical variables represent categories or groups.
What were the frequencies observed when tossing a die 100 times?
1: 18, 2: 12, 3: 32, 4: 16, 5: 12, 6: 10.
What is a sample?
A portion of the population selected for analysis.
What is the standard deviation of items sold?
229.54 items.
How is the expectation of a discrete random variable X denoted?
It is denoted by μX or E(X).
What does the mean of X represent in the long run?
It represents the average value of X.
Why is an updated sampling frame important?
It ensures every element has a chance to be selected for probability samples.
What is the goal of selecting a 'good representative' sample?
To ensure the sample mean is reasonably close to the unknown population mean.
To how many decimal places should answers be corrected when necessary?
4 decimal places.
What is the average weekly profit gained by selling PhotoC?
The average weekly profit is $5831.
What if the index i is an integer?
The p-th percentile is the average of the values at the i-th and (i+1)-th positions.
What is the population size denoted by?
N (N = 3000).
What is used to summarize a Binomial variable?
Probability distribution function, expected value, variance, and standard deviation.
How can we generate the probability distribution function for the number of books borrowed from a library?
By using the relative frequency from the library's borrowing records.
What is the probability distribution function for the number of books borrowed (1 to 8)?
1: 0.02, 2: 0.07, 3: 0.15, 4: 0.28, 5: 0.33, 6: 0.10, 7: 0.03, 8: 0.02.
What is the empirical probability of observing an odd number when tossing an unfair die?
P(odd) = 0.4333.
How do you input frequency for multiple observations on the Casio fx-50FH calculator?
Input the repeated value followed by SHIFT, then 4, and DT.
What is the significance of the probabilities in the expectation formula?
They act as weights for the outcomes in the calculation of the expected value.
What is the standard deviation of Y if σ(X) = 1.0618?
σ(Y) = |4340|σ(X) = $4608.38.
What is the 40th percentile in the given example?
574.5 items.
What type of variable is gender in this context?
Categorical variable.
How is the interquartile range (IQR) of Y related to the IQR of X?
IQR(Y) = |b| * IQR(X)
What is the 90th percentile in the given example?
904 items.
