Statistics
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| A population | show |
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| Random sampling: | 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. | show 🗑
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| Stratified sampling: | show |
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| measure of central tendency | is just a mathematical and rather posh way of saying "averages". | show 🗑
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| The Mode | show |
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| The Median | 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. | show 🗑
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| The Mean | show |
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| Ex | show |
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| grouped frequency table->find MEAN | show |
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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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| m-and-leaf diagram | show |
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| show | 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. | 1.The ‘box’ part is drawn from the lower quartile to the upper quartile. The median is then drawn within the box.
2.The ‘box’ shows the inter-quartile range, which houses the middle half of the data.
3.The ‘whiskers’ are then drawn to the lowest and hig
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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: | There is a greater proportion of the data at the lower end. | show 🗑
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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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| show | is kind of like a running total. We add each frequency to the ones before to get an ‘at least’ total. | (blank)
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| show | cumulative frequencies (‘at least’ totals) are plotted against the upper class boundaries to give us a cumulative frequency curve. | (blank)
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| show | The probability that an event, A, will happen is written as | (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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| mutually exclusive | show | 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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| 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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| show | P(R I F) | P(R n F) / P(F)
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| discrete random variable | 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. | show 🗑
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| random variable | show | (blank)
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| exclusive events Rewrite -> Sum? | E P(X = x) = 1 -> always sum to 1 | show 🗑
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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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| 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 | show | (blank)
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| show | aE(X) + b | (blank)
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| show | a | (blank)
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| show | 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. | (blank)
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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 | 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 | (X - u) / o- | show 🗑
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| Normal Distribution Graph | show | (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 | this Greek letter just describes the area under the bell from that point! | (blank)
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| line of best fit’ | show | (blank)
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| linear correlation | show | (blank)
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| show | (blank) | (blank)
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| show | Sxy / Syy | (blank)
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| Regression Line y on x->Formula for b: | show | (blank)
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| Independent/dependent variables | show | (blank)
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| product moment correlation coefficient | r -> is a measure of the degree of scatter.->will lie between -1 and 1. | show 🗑
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| "r" | show | (blank)
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| show | €x times P(X = x) / or € f(x)P(X = x) | (blank)
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Created by:
1sabelle