Statistics
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| A population | 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. | show 🗑
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| show | this method gives every item of the population an equal chance of selection. This can be done in various ways for example by simply picking out of a hat or by using a random number generator on a calculator. |
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| Stratified sampling: | some populations are naturally split into a number of strata (kind of like sub groups). We can separate the strata and find what proportion of the population is in each stratum. We can then select a random sample from each stratum proportional to its size | show 🗑
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| show | is just a mathematical and rather posh way of saying "averages". |
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| The Mode | It is the piece or pieces of data that occur most often. | show 🗑
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| show | The median is the middle piece of data when the data is in numerical order.->With 50 pieces of data, even, we must find halfway and the next value. In this case, the 25th and 26th values. The median will be halfway between these values. |
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| The Mean | The mean of a set of data is the sum of all the values divided by the number of values. - Ex x=----- n | show 🗑
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| Ex | just means the sum of all the x’s - for instance, add all the bits of data together. | show 🗑
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| grouped frequency table->find MEAN | show |
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| (f) | show |
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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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| Formula standart deviation | square root of ((the sum of x2 - ((mean of x)squared)) divided by the number of units | show 🗑
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| "o- 2" definition | The variance is the square of the standard deviation. | show 🗑
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| The variance | show |
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| m-and-leaf diagram | show |
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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: | show | (blank)
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| show | There is a greater proportion of the data at the lower end. | (blank)
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| show | Values of data are usually labelled as outliers if they are more than 1.5 times of the inter-quartile range from either quartile. | (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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| frequency density | show | frequency / class with
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| Cumulative frequency | show | (blank)
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| cumulative frequency curve. | show | (blank)
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| P(A) | show | (blank)
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| show | The probability that the event A, does not happen is called the complement of A and is written as A' | (blank)
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| show | 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 | Exclusive events will involve the words ‘or’, ‘either’ or something which implies ‘or’.->Remember ‘OR’ means ‘add’.
P(A or B) = P(A) + P(B)
P(A u B) = P(A) + P(B)
P(A u B u C) = P(A) + P(B) + P(C)
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| Independent Events | 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 | show 🗑
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| show | P(R I F) | P(R n F) / P(F)
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| discrete random variable | show | 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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| show | is a variable which takes numerical values and whose value depends on the outcome of an experiment | (blank)
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| show | E P(X = x) = 1 -> always sum to 1 | (blank)
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| show | 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. | (blank)
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| Cumulative distribution function | show | (blank)
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| show | 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’.. | E(X) = € xP(X = x) -> You multiply each value of x with its corresponding probability. If we then add all these up we obtain the expectation of X. This is best seen in an example.
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| uniform distribution | 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. | show 🗑
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| symmetry of the table | 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. | show 🗑
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| Expectation of any function of x | show | (blank)
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| E(aX + b) Equals | aE(X) + b | show 🗑
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| show | a | (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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| show | -> mean -> u -> Example of Calculation->(0 x 0.1) + (1 x 0.2) + (2 x 0.5) + (3 x 0.2) | (blank)
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| Var(aX) Equals | show | Var(2X) = 22 x Var(X)
= 4 x 2.5 = 10
Var(4X – 3) = 42 x Var(X)
= 16 x 2.5 = 40
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| show | a2Var(X) This means by knowing just the variance, Var(X), we can calculate other variances quickly. Example: | Var(2X) = 22 x Var(X)
= 4 x 2.5 = 10
Var(4X – 3) = 42 x Var(X)
= 16 x 2.5 = 40
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| The Standard Deviation | The square root of the Variance is called the Standard Deviation of X. standard deviation is given the symbol o- | show 🗑
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| convert any normal distribution of X into the normal distribution of Z | show | (blank)
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| Normal Distribution Graph | 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. | show 🗑
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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 | this Greek letter just describes the area under the bell from that point! | (blank)
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| line of best fit’ | Any line of best fit must go through the mean of x, and the mean of y. | show 🗑
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| show | If all (or nearly all) of these points seem to lie in a straight line | (blank)
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| Equation of regression line | show | (blank)
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| Regression Line x on y->Formula for b: | Sxy / Syy | show 🗑
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| Regression Line y on x->Formula for b: | Sxy / Sxx | show 🗑
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| Independent/dependent variables | show | (blank)
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| show | r -> is a measure of the degree of scatter.->will lie between -1 and 1. | (blank)
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| "r" | The product moment correlation coefficient, r, is a measure of the degree of scatter.->will lie between -1 and 1. | show 🗑
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| Calculate E(X) | €x times P(X = x) / or € f(x)P(X = x) | show 🗑
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Created by:
1sabelle