| Sample Mean (1 dp) | Sample Standard Deviation (3 sig figs) | Median (exact value) | Interquartile Range (exact value) |
|---|---|---|---|
| [[0]] | [[1]] | [[2]] | [[3]] |
Sample mean: The sample mean is $\\frac{\\var{sum(r0)}}{\\var{len(r0)}} = \\var{precround(mean(r0),1)}$ to 1 decimal place.
\nSample standard deviation: The sample standard deviation is $\\var{stdev(r0,true)}=\\var{siground(stdev(r0,true),3)}$ to 3 significant figures.
\nIf you order the data in increasing order you get the following table:
\n| $\\var{r1[0]}$ | \n$\\var{r1[1]}$ | \n$\\var{r1[2]}$ | \n$\\var{r1[3]}$ | \n$\\var{r1[4]}$ | \n$\\var{r1[5]}$ | \n$\\var{r1[6]}$ | \n$\\var{r1[7]}$ | \n
| $\\var{r1[8]}$ | \n$\\var{r1[9]}$ | \n$\\var{r1[10]}$ | \n$\\var{r1[11]}$ | \n$\\var{r1[12]}$ | \n$\\var{r1[13]}$ | \n$\\var{r1[14]}$ | \n$\\var{r1[15]}$ | \n
| $\\var{r1[16]}$ | \n$\\var{r1[17]}$ | \n$\\var{r1[18]}$ | \n$\\var{r1[19]}$ | \n$\\var{r1[20]}$ | \n$\\var{r1[21]}$ | \n$\\var{r1[22]}$ | \n$\\var{r1[23]}$ | \n
Denote the ordered data by $x_j$, thus $x_{10}=\\var{r1[9]}$ for example.
\nMedian: The median lies between the 12th and 13th entries in the ordered table and is given by:
\n\\[0.5\\times x_{12}+0.5\\times x_{13} = 0.5\\times\\var{r1[11]}+0.5\\times \\var{r1[12]}=\\var{median}\\]
\nInterquartile range: As there is an even number of values, the Lower Quartile will lie between two values. Its position is calculated by finding
\n\\[\\frac{n+1}{4}=\\frac{\\var{n+1}}{4}=6\\frac{1}{4}\\]
\nHence the Lower Quartile lies between the 6th and 7th entries in the ordered table.
\nIt is \\[0.75\\times x_6+0.25\\times x_7 = 0.75\\times\\var{r1[5]}+0.25\\times \\var{r1[6]}=\\var{lquartile}\\]
\nOnce again as there is an even number of values, the Upper Quartile will lie between two values and its position is calculated by finding
\n\\[\\frac{3(n+1)}{4}=\\frac{\\var{3*(n+1)}}{4}=18\\frac{3}{4}\\]
\nHence the Upper Quartile lies between the 18th and 19th entries in the ordered table.
\nWe find it is \\[0.25\\times x_{18}+0.75\\times x_{19} = 0.25\\times\\var{r1[17]}+0.75\\times \\var{r1[18]}=\\var{uquartile}\\]
\nThe interquartile range is defined to be
\n\\[ \\text{Upper Quartile} – \\text{Lower Quartile} \\]
\nand so in this case we have:
\n\\[ \\text{Interquartile range} = \\var{uquartile}-\\var{lquartile}=\\var{interq} \\]
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\n| $\\var{r0[0]}$ | \n$\\var{r0[1]}$ | \n$\\var{r0[2]}$ | \n$\\var{r0[3]}$ | \n$\\var{r0[4]}$ | \n$\\var{r0[5]}$ | \n$\\var{r0[6]}$ | \n$\\var{r0[7]}$ | \n
| $\\var{r0[8]}$ | \n$\\var{r0[9]}$ | \n$\\var{r0[10]}$ | \n$\\var{r0[11]}$ | \n$\\var{r0[12]}$ | \n$\\var{r0[13]}$ | \n$\\var{r0[14]}$ | \n$\\var{r0[15]}$ | \n
| $\\var{r0[16]}$ | \n$\\var{r0[17]}$ | \n$\\var{r0[18]}$ | \n$\\var{r0[19]}$ | \n$\\var{r0[20]}$ | \n$\\var{r0[21]}$ | \n$\\var{r0[22]}$ | \n$\\var{r0[23]}$ | \n