Fixed subscript in quartile definition

whitead · May 7, 2018 · 061ee69 · 061ee69
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diff --git a/unit_7/lectures/lecture_1.pdf b/unit_7/lectures/lecture_1.pdf
diff --git a/unit_7/lectures/lecture_1.tex b/unit_7/lectures/lecture_1.tex
@@ -83,7 +83,7 @@ \subsection{Median}
 
 \subsection{Quartiles}
 
-The median indicates the divsion between the lower 50\% of values and the upper 50\% of values. We can define two more numbers that indicate the lower 25\% and upper 25\%. These dividing numbers are called quartiles and are indicated as $Q_1$, $Q_2$ (also the median), and $Q_3$. The quartiles need not be actual values in the data, just like how sometimes the median is the arithmetic mean if we have an even number of values. For example, consider the numbers 4, 6, 13, 22. The median, which is also $Q_2$, is $(6 + 13) / 2 = 9.5$. $Q_1$ is the median of the values below $Q_2$: the median of 4, 6. Thus $Q_1 = 5$. Similarily, $Q_4$ is the median of 13 and 22: 17.5. Now arrange the data and quartiles: $ 4, |\,\underbrace{5}_{Q_1}\,|, 6, |\,\underbrace{9.5}_{Q_2}\,|, 13, |\,\underbrace{17.5}_{Q_3},\,| 22$. Notice how the quartiles split the data into 4 groups, each containing 25\% of the values.
+The median indicates the divsion between the lower 50\% of values and the upper 50\% of values. We can define two more numbers that indicate the lower 25\% and upper 25\%. These dividing numbers are called quartiles and are indicated as $Q_1$, $Q_2$ (also the median), and $Q_3$. The quartiles need not be actual values in the data, just like how sometimes the median is the arithmetic mean if we have an even number of values. For example, consider the numbers 4, 6, 13, 22. The median, which is also $Q_2$, is $(6 + 13) / 2 = 9.5$. $Q_1$ is the median of the values below $Q_2$: the median of 4, 6. Thus $Q_1 = 5$. Similarily, $Q_3$ is the median of 13 and 22: 17.5. Now arrange the data and quartiles: $ 4, |\,\underbrace{5}_{Q_1}\,|, 6, |\,\underbrace{9.5}_{Q_2}\,|, 13, |\,\underbrace{17.5}_{Q_3},\,| 22$. Notice how the quartiles split the data into 4 groups, each containing 25\% of the values.
 
 Let's do one more example with an odd number of data points. Consider: 8, 1, -2, 3, 5, 11, 3. First rearrange:
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