Notice that each of the measured values, x_0 <\/span> to x_8 <\/span> , contributes to more than one of the averages. In turn, the errors on each of the measured values will affect the value of more than one of the averages. For example, each of the measured values x_1 <\/span> and x_2 <\/span> is used in the calculation of both \\bar{x}_a <\/span> and \\bar{x}_b <\/span> . The result of this is that the errors in \\bar{x}_a <\/span> and \\bar{x}_b <\/span> are correlated. On the other hand, notice that there is no error correlation between \\bar{x}_h <\/span> and \\bar{x}_b <\/span> , because they do not have any measured values in common<\/p>\r\n\r\n\r\n\r\n If we now focus on \\bar{x}_d <\/span> , we can visualise the number of measured values in common with the other averages by looking at the graph below, which shows the fraction of common measured values that \\bar{x}_d <\/span> shares with the other averages we introduced in the diagram above.<\/p>\r\n\r\n\r\n\r\n We can use this graph to infer something about the error correlation between \\bar{x}_d <\/span> and our other averages: the \u2018closer\u2019 the two averages, the greater the number of measured values in common, and the greater the error correlation. Conversely, two averages that are \u2018further away\u2019 have less values in common and weaker error correlation, and averages that are sufficiently far apart have no error correlation.<\/p>\r\n\r\n\r\n\r\n![\"\"](\"https:\/\/research.reading.ac.uk\/fiduceo\/wp-content\/uploads\/sites\/129\/2019\/07\/tutorial4_figure1-1-1024x765.png\")
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