Statistics
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| show | is the set of all the possible items to be observed. example: Whilst investigating the height of males in Wales, the population would be the height of all the males in Wales. |
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| Random sampling: | show |
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| Stratified sampling: | show |
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| show | is just a mathematical and rather posh way of saying "averages". |
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| show | It is the piece or pieces of data that occur most often. |
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| The Median | show |
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| show | The mean of a set of data is the sum of all the values divided by the number of values. - Ex x=----- n |
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| show | just means the sum of all the x’s - for instance, add all the bits of data together. |
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| show | We can however, find an estimate of the mean by assuming each footballer is the height halfway within his interval |
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| show | means frequency |
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| show | standart deviation->gives a measure of how the data is dispersed about the mean->the lower the standard deviation, the more compact our data is around the mean |
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| show | square root of ((the sum of x2 - ((mean of x)squared)) divided by the number of units |
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| "o- 2" definition | The variance is the square of the standard deviation. | show 🗑
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| The variance | is the square of the standard deviation. | show 🗑
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| show | presenting it in an easy and quick way to help spot patterns in the spread of data->They are best used when we have a relatively small set of data and want to find the median or quartiles |
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| Box-and-whisker plots (or boxplots) | These are very basic diagrams used to highlight the quartiles and median to give a quick and clear way of presenting the spread of the data. | show 🗑
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| Negatively skewed distribution: | There is a greater proportion of the data at the upper end. | show 🗑
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| Positively skewed distribution: | show | (blank)
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| Outliers | show | (blank)
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| show | Histograms are best used for large sets of data, especially when the data has been grouped into classes. They look a little similar to bar charts or frequency diagrams. ->In histograms, the frequency of the data is shown by the area of the bars and not ju | (blank)
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| show | The vertical axis of a histogram is labelled | frequency / class with
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| Cumulative frequency | show | (blank)
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| cumulative frequency curve. | cumulative frequencies (‘at least’ totals) are plotted against the upper class boundaries to give us a cumulative frequency curve. | show 🗑
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| P(A) | The probability that an event, A, will happen is written as | show 🗑
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| complement of A | The probability that the event A, does not happen is called the complement of A and is written as A' | show 🗑
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| mutually exclusive | Two events are mutually exclusive if the event of one happening excludes the other from happening->they both cannot happen simultaneously->When a fair die is rolled find the probability of rolling a 4 or a 1. P(4 u 1) = P(4) + P(1)=>1/6 +1/6=>1/3 | show 🗑
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| show | Two events are independent if the occurrence of one happening does not affect the occurrence of the other.->P(A and B) = P(A) ' P(B) ->P(A n B) = P(A) ' P(B) Independent events will involve ‘and’, ‘both’,"either"->means multiply | A coin is flipped at the same time as a dice is rolled. Find the probability of obtaining a head and a 5.->P(H n 5)=P(H)'P(5)=> 1/2 x 1/6=> 1/12
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| How do you write Find the probability that given he falls P(F) it was a rainy day P(R). | P(R I F) | show 🗑
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| show | A random variable is a variable which takes numerical values and whose value depends on the outcome of an experiment. It is discrete if it can only take certain values. | Capital letters are used to denote the random variables, whereas lower case letters are used to denote the values that can be obtained.
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| random variable | show | (blank)
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| show | E P(X = x) = 1 -> always sum to 1 | (blank)
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| Probability density function | Sometimes we are given a formula to calculate probabilities. We call this the probability density function of X or the p.d.f. of X. | show 🗑
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| show | ‘Cumulative’ gives us a kind of running total so a cumulative distribution function gives us a running total of probabilities within our probability table. The cumulative distribution function, F(x) of X is defined as: F(x) = P(X < x) | (blank)
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| Expectation | The expectation is the expected value of X, written as E(X) or sometimes as u->The expectation is what you would expect to get if you were to carry out the experiment a large number of times and calculate the ‘mean’.. | show 🗑
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| show | This is a ‘special’ discrete random variable as all the probabilities are the same.->it is possible to calculate the expectation by using the symmetry of the table. The expectation, E(X) is calculated by finding the halfway point. | (blank)
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| show | With uniform distributions it is possible to calculate the expectation by using the symmetry of the table. The expectation, E(X) is calculated by finding the halfway point. | (blank)
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| Expectation of any function of x | E[f(x)] = € f(x)P(X = x) | show 🗑
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| show | aE(X) + b | (blank)
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| E(a) Equals | show | (blank)
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| variance | is a measure of how spread out the values of X would be if the experiment leading to X were repeated a number of times. | show 🗑
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| E(X) | -> mean -> u -> Example of Calculation->(0 x 0.1) + (1 x 0.2) + (2 x 0.5) + (3 x 0.2) | show 🗑
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| Var(aX) Equals | a2Var(X) | show 🗑
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| Var(aX + b) Equals | a2Var(X) This means by knowing just the variance, Var(X), we can calculate other variances quickly. Example: | show 🗑
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| The Standard Deviation | show | (blank)
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| convert any normal distribution of X into the normal distribution of Z | show | (blank)
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| show | much of the data is gathered around the mean. The distribution has a characteristic ‘bell shape’ symmetrical about the mean. ->The area of the bell shape = 1. | (blank)
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| show | is an important measure of the spread of our data. The greater the standard deviation, the greater our spread of data. | (blank)
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| § | show | (blank)
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| show | Any line of best fit must go through the mean of x, and the mean of y. | (blank)
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| linear correlation | show | (blank)
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| Equation of regression line | show | (blank)
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| Regression Line x on y->Formula for b: | show | (blank)
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| show | Sxy / Sxx | (blank)
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| show | With the above data, x looks to be controlled, where y appears to be dependent on an experiment and x. In this case, we say that x is an independent variable and y a dependent variable. As x appears controlled and accurate we only need to calculate the re | (blank)
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| product moment correlation coefficient | show | (blank)
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| show | The product moment correlation coefficient, r, is a measure of the degree of scatter.->will lie between -1 and 1. | (blank)
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| Calculate E(X) | show | (blank)
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Created by:
1sabelle