# The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?

The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?
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wintern90
${n}_{1}=16$
${n}_{2}=14$
$\overline{{x}_{1}}=107$
$\overline{{x}_{2}}=112$
${s}_{1}=10$
${s}_{2}=8$
Pooled standard deviation is defined as an estimate of standard deviation when different groups are assumed to have the same standard deviation.
The pooled variance is given by:
${S}_{p}^{2}=\frac{\left({n}_{1}-1\right){s}_{1}^{2}+\left({n}_{2}-1\right){s}_{2}^{2}}{{n}_{1}+{n}_{2}-2}\phantom{\rule{0ex}{0ex}}=\frac{\left(16-1\right){10}^{2}+\left(14-1\right){8}^{2}}{16+14-2}\phantom{\rule{0ex}{0ex}}=\frac{2332}{28}\phantom{\rule{0ex}{0ex}}=83.2857$
The pooled sd is given by:
$sd=\sqrt{83.2857}\phantom{\rule{0ex}{0ex}}=9.1261$
Darian Hubbard