Statistics Flashcards
What Latin word is statistics derived from?
Status.
What’s the purpose of statistics?
To help us get information out of large amounts of numbers and data.
What 2 main branches does statistics fall under? And which is this module about?
- Descriptive statistics; which focuses on collecting, summarising, and presenting a set of data.
- Inferential statistics; analyses sample data to draw concultions from a population to make decisions.
This module focuses on descriptive statistics.
Why does statistics actually exist?
Because psychologists, engineers, medical researchers and economists built it, and they build it because they needed it.
Another term for whole numbers and what do they consist of?
Integers. 0-9
What’s the numerator and what’s another term for it?
It’s also called the dividend. The one on top.
What’s the denominator and what’s another term for it?
The one at the bottom. Divisor.
What’s another term for dividing?
Quotient
What’s a proper and improper fraction?
A proper fraction is one which the numerator is less than the denominator.
How do you add fractions?
1/5 + 2/5 = 1+2/5
What is HCF? And where is it used? And how’s it work?
Highest common factor. Used to multiply fractions.
How do you divide fractions?
What 3 components do decimals consist of?
An integer, followed by a decimal point, followed by another integer.
How do you add decimals?
How do you times decimals?
How do you divide decimals?
What does percent mean?
Per hundred.
How do you calculate a percentage rate of an amount?
R = P/B
Portion/Base
What is an exponent?
A number that is written as a superscript to another number called the base.
How do you times and divide exponents?
Solve x
What does 4 ^ 0 = to?
1.
What’s 0 ^ 0?
Undefined.
Define statistics.
Statistics is the scientific method that enables us to collect, organize, analyse, and interpret data in order to make decisions as responsibly as possible.
What’s the 2 main characteristics of Statistics?
- Data; numerical facts
- Information; knowledge communicated
Describe the decision-making process.
- Collect relevant information as reliable as possible.
- Select parts most helpful.
- Make the decisions as sensibly as possible.
- Perceive the risks in the decision and evaluate the corresponding risks of alternative decisions.
What’s statistics used for in economics and commerce?
- To assist in designing statistical methodology for best effect.
- To draw inferences and predict the future.
What is data?
Data is a scientific term for a collection of facts such as values or measurements for a specific topic of interest.
What’s are data sets?
Are collections of organized data that can be used for analysis such as, population, and sample.
What is population in statistics?
The totality of the population of all objects that are interested in studying at any one moment.
What’s a parameter?
It’s a numerical value that summarises a characteristic of the entire population.
Define sample.
A subset of the population which will be expected to be a good representation of the population.
Define a statistic.
It’s a numerical value used to describe or summarise the characteristics of a sample.
What is a variable?
A variable is a phenomenon which changes with respect to the influence of other phenomena or objects.
What 2 types of variables do you get and briefly explain them.
- Dependent variables; their magnitude depends on the magnitude or the presence of other variables.
- Independent variables; are those phenomena which are capable of influencing other variables without being themselves influenced.
What is a model?
A theoretical construction of all expected interrelationships of facts and figures which cause and affect any natural physical or social phenomenon.
What do models attempt?
They attempt to construct a simplified explanation of the complex reality in a manner which can be easily understood, and whose nature can generally be said to be possible at all times.
Consumers can only be modelled because we can’t lock them up.
What is an index?
It’s an imprecise and imperfect measure of some underlying concept variable which is not directly measurable, which is only capable of indicating a trend.
What acronym is there for the basic operations of algebra?
BODMAS
Brackets, Orders, Division, Multiplication, Addition, and finally Subtraction.
What types of variables do you get? And what are the off sets of them?
- Qualitative variables; descriptive information that can be devided into categories. (Colour, gender, type of vehicle).
- Quantitative variables; are measured numerically which can be split into 2:
- Discrete variables; whole
numbers. (No. of students in a class). - Continuous variables. (A person’s height & time in a race).
- Discrete variables; whole
What are the 2 main groups of data?
- Primary data; collected especially for this soecific survey that is being conducted.
- Secondary data; data already collected from elsewhere, for some other purpose, but which can be used.
What ways can statistical data be obtained?
Measurements and counts.
What categories can data be classified into? Explain.
- Nominal data; lowest level of measurement. Classify data qualitatively by name. (Cats as black and white). Impossible to arrange and rate them.
- Ordinal data; differentiation with size, has magnitude and direction. Can be arranged in order but not rated. (Low income, Middle Income, High income).
- Interval data; has magnitude and direction. It has equal intervals but the weakness of this data is that the position of 0 is unclear. (Temperature). It can be rated but ratios are difficult to compute.
- Ratio data; the highest level of measurement, with transitivity; magnitude and direction; equal interval qualities; and the zero can be identified. Ratios are possible. (Height, weight, profit, age).
Why do we sample data?
- Unpractical to analyse all data.
- Not physically possible.
- Too expensive
- Situation, sampling needs to be done quickly.
What are some things to keep in mind in order to collect data most efficiently?
- Sample it from the population.
- Sample must be unbaised otherwise ti will be worthless.
- Implement sample rules to help eliminate bias in sampling.
- Sampling errors are inevitable. Asses how much variation can be expected to occur.
- Sample randomly
What are some rules that will help prevent biased sampling?
- Do not only use people that volunteer.
- Do not choose a sample using a method that omits segments of the population.
- Do not use people in the sample only because they are available.
- The person selecting the sample should not have a vested interest in the results.
What are some questions to ask before sampling data?
- What should the size of the sample be?
- What precisely are the members from which the sample is to be chosen.
- How should the members be selected for inclusion?
Sample size will depend on the type of problem and the desired accuracy?
What are some ways conduct random sampling correctly?
*Random numbers can be generated by a software program or a calculator.
*Population members are assigned a number.
*Sample is then chosen to randomly chosen numbers.
What are other methods of sampling other than random sampling and explain them.
- Systematic sampling: by selecting every nth time after a random start. Sampling intervals.
- Quota sampling: population is divided into subgroups based on characteristics. Then researchers select representatives from the quotas non-randomly.
- Stratified sampling: dividing the population into strata or categories. Random samples are then taken from each stratum or category.
- Cluster sampling: a non-random sampling method that involves dividing the population into pre-existing groups and then randomly selecting entire clusters as a sample.
- Multistage sampling: a probability sampling method which involves dividing the population into a number of sub-populations and then selecting a small sample of these sub-populations at random. Each sub-population is then divided further, and then a small sample is again selected at random.
How should a survey or questions be designed to maximize efficiency?
*Questions should be designed that allow the person the freedom to give his or her honest opinion.
*Questions should be open ended, multiple choice and open for interpretation.
*The person completing the questionnaire should do so confidentiality, as their opinions should not be made known to others.
The type of visual representation you choose depends on what?
It depends on the type of variables you are dealing with within your data set. Nominal, ordinal, Interval, ratio data.
What are some data preparation rules?
Data presented must always be:
* Factual
*And relevant
Before presentation always check the source of the data to ensure that the:
*Data has been accurately transcribed
*Figures are relevant to the problem
What are some important points that should be followed when constructing a table?
- A clear label for the table.
- The type of information in the actual table should be properly titled.
- Rows and columns should be precise, and units of the values included.
- Clearly state the units.
- Show percentages and ratio where appropriate.
- Categories should not overlap.
- Correctness of calculations should be verified.
- Omit any unnecessary or irrelevant data.
- Use your imagination and common sense.
Why are tables better than narratives for data?
Because they are much more compact and helps us distiguish patterns.
In what way are graphs better in representing data than tables?
They better depict relationships between variables and more than one set of data can be displayed on a graph.
What are some points to keep in mind when constructing a graph?
- Give an appropriate title.
- Label the axes x & y with units of measurement.
- Do not plot too many curves on the same set of axes.
- Accompany the graph with the table of data.
- Show the 0 on each scale.
What is a pie chart use for?
To give a visual presentation of data to indicate the proportions that make up a given total.
What is a pie chart?
A circle that is divided into sectors by lines, in such a way that the area of each sector is proportional to the size of the quantity represented by that sector.
What is a bar chart?
A series of rectangular bars where the length of each bar represents the actual magnitude of the respective quantities.
What are some guidelines for preparing a bar chart?
- Make widths of each bar equal.
- Clearly label the axes
- Include footnotes, source data and tables
What’s the purpose of creating a multiple bar chart?
To emphasize comparison.
What is a pictogram?
A graph in which data is displayed using pictures.
What’s a scatter diagram used for?
To display the relationship between 2 quantitative variables. It displays data points as dots on a 2 dimensional graph. For example, the relationship between advertising and sales.
Which axes does the dependant and independent variables go on?
Independent (the cause) - x-axis
Dependent (the effect) - y-axis
What is a positive relationship between to variables refer to?
This means their values tend to increase together and decrease together.
What’s the difference between a non-linear & linear relationship?
What is a negative linear relationship?
When 2 variables move in opposition directions and the scatter diagram consists of points that appear to cluster around a straight line.
What is raw data and what’s wrong with it?
Raw data is unprocessed data and is difficult to distinguish any pattern in the data due to to many variables.
What’s the purpose and advantages of a frequency table?
- It solves the problem that raw data brings by summarising data in tables that report how often certain sextions appear. This helps us identify patterns and make it more understandable.
- It also helps us locate figures more quickly.
- Makes it easier to compare different classes.
What elements do Frequency tables have?
- Classes or class intervals; represent the possible data values that the variables assume AKA categories (k)
- Class midpoint; represents the middle value of a class interval.
- Frequencies; represent the number of times that observation fall within a specified class.
- Percentage frequencies; of the total sample size.
What are some rules to follow when constructing a frequency table?
- The class intervals must never overlap.
- Intervals should be if the same width.
- The first or/and last class interval could be open ended but avoided as much as possible.
- If no observations in a particular interval, it should still be included to avoid misleading impression of the data.
- Sum of frequencies equals total number of observations.
What’s the symbol for population mean.
What’s the symbol for a sample mean?
What’s the formula for calculating the sample mean?
What’s the formula for calculating the mean in a grouped frequency distribution?
What’s the formula for calculating the geometric mean?
What’s the formula for calculating the mode in a grouped frequency distribution? And what do those elements all represent?
What’s the symbol for the median?
What’s the formula for calculating the median?
What’s the formula for calculating the median in a grouped frequency distribution?
What are the formulas for calculating the 3 Quartiles for organising raw data?
What’s the formula for calculating an exact percentile?
What formula do you use when calculating a percentile when it’s not a whole number?
What’s the formula for the percentile in grouped frequency distribution data?
What are the 3 most common shapes of distribution? And explain each.
- Symmetric shape; the distribution is identical in both sides of its central point where each left and right sides mirror eachother. Mean=median=mode.
- A uniform or rectangular distribution; is a symmetric distribution with equal or approximately equal frequencies for each class.
- A skewed-to-the-right distribution positively skewed); has a longer tail on the right side. Mode<Median<Mean.
- A skewed-to-the-right distribution (negatively skewed); has a longer tail on the left side. Mean<Median<Mode.
What are the 3 most common shapes of distribution? And explain each.
- Symmetric shape; the distribution is identical in both sides of its central point. Mean=median=mode.
- A uniform or rectangular distribution; is a symmetric distribution with equal or approximately equal frequencies for each class.
- A skewed-to-the-right distribution positively skewed); has a longer tail on the right side. Mode<Median<Mean.
- A skewed-to-the-right distribution (negatively skewed); has a longer tail on the left side. Mean<Median<Mode.
How do we best represent the following levels of measurement: nominal data, ordinal data, Interval/Ratio data?
What’s the symbol for standard deviation? And what’s the formula for calculating it?
What’s the formula for standard deviation of a sample?
How do you calculate the standard deviation for frequency distribution?
How do you calculate standard deviation for a sample from a grouped frequency distribution?
What is the Empirical rule? And when can it be used?
The Empirical rule states:
* About 68% of the data lie within one standard deviation.
* About 95% of the data lie within 2 standard deviations of the mean.
* About 99.7% if the data lie within 3 standard deviations of the mean.
The Empirical rule can only be used when the histogram is symmetrical.
What’s the formula for the standard score? And whats it’s symbol?
What’s the formula for coefficient variation?
How is probability expressed in a formula?
P(A) = r/n
r= number of favourable outcomes
n= number of trials
A= is the favourable event.
What is the formula for conditional probability?
It indicates “on condition that”.
Discuss the rules of probability.
-
The multiplication rule. If A and B are independent events, the probability of joint occurrence of these 2 events is equal to the product of the probability of the occurrence of each one of them. As long as they are independent.
P(H1 and H2) = P(H1) x P(H2) = 0.5 x 0.5 = 0.25
This reduces the size of the fraction due to the difficulty in having emsjch a lucky coincidence occuring in real life. -
Addition rule. When one is faced with alternative events, each one of which is a success, the chances if success increase because the investigator is satisfied by any of the successes.
P(A or B) = P(A) + P(B)
Area of overlap between 2 needs to be minused from eachother.
Example, 4 A’s and 4 Hearts in a deck. There’s 1 card that over laps (queen of hearts) that needs to be minused from the probability.
What is the formula for permutation?
What is the formula for permutation?
What’s the formula for combinations?
What’s the formula for regression analysis?
What’s a perfect positive correlation look like?
What does a negative correlation look like?
What does a positive direct relationship look like?
What does a positive direct relationship look like?
What does a negative indirect linear correlation look like?
What does a positive direct linear correlation look like with r->0?
What is Pearson’s correlation formula?
What’s the formula for an index number? And give some examples.
What’s the formula for price index?
What’s the formula for the quantity index?
What are fixed weighted index numbers? And what’s formula?
A type of index number that uses a fixed set of weights from a specific base period to calculate changes in a variable over time. They don’t need to be necessarily be drawn from the same period and these weights remain constant regardless of changes.
What’s a simple weighted index? And what’s its formula?
This places the base heat for both price and quantity in the numerator. Which runs the risk of a lack of representivity in the base period.
What is the laspeyres price index and what’s its formula?
Quantities at base period levels are held constant.
What’s the formula for laspeyres quantity index?
What’s Paasche index’s formula?
What’s Paasche index’s formula?
