(Solved): Please answer questions 1 and 2 correctly using the right formulas. ONLY USE FORMULAS THAT ARE SHOWN ...

1. For the following set of data find the mean, median and mode $4,5,12,14,19,7,12,23,7,17,15,21$ 2. A shoe store found for women's shoe sizes the mean is 7.5 , the mode 8 , and median 7.5. Which measure of central tendency would be most beneficial to the manager when ordering more inventory? Why? Statistics Population size $=\mathrm{N}$ Sample size $=n$ (\# 27) Population mean: $?=\frac{?x}{N}$ (\# 28) Sample mean: $\stackrel{?}{x}=\frac{x_1+x_2+\dots +x_n}{n}=\frac{?x}{n}$ (\# 29) Population variance: ${?}^2=\frac{?(X??{)}^2}{N}$ (\# 30) Sample variance: $s^2=\frac{?(x?\stackrel{?}{x}{)}^2}{n?1}$ (\# 31) Population standard deviation: $?=\sqrt{{?}^2}$ (\# 32) Sample standard deviation: $s=\sqrt{s^2}$ (\# 33) Range $=\max ?\min$ (\# 34) Inter-quartile range: $IQR=Q_3?Q_1$ (\# 35) To find $z$-score for a given $x$ value: $\begin{array}{l}z=\frac{x?\stackrel{?}{x}}{S}\text{ or }z=\frac{x??}{?}\\ x=\stackrel{?}{x}+zS\text{ or }x=?+z?\end{array}$ (\# 36) To find $x$-value for a given $z$-score: (\# 37) Emprical Rule (68-95-99.7 Rule): For any bell-shaped symmetric distribution: - Approximately $68\%$ of the data value occur within $\stackrel{?}{x}\pm 1s$ (or $?\pm 1?$ ) - Approximately $95\%$ of data values lie within $\stackrel{?}{x}\pm 2s$ (or $?\pm 2?$ ) - Approximately $99.7\%$ of data values lie within $\stackrel{?}{x}\pm 3s$ (or $?\pm 3?$ ).