QUESTION TWO
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2.1 Rank each of the following value in order of smallest to largest:
1. the upper quartile.
II. the median.
III. the \( 20^{\text {th }} \) percentile.
IV. decile 6 .
V. the 0.38 fractile.
VI. the \( 70^{\text {m }} \) percentile.
VII. the lower quartile.
2.2. The price (in rands) in June of a \( 1 \mathrm{~kg} \) packet of laundry in KwaDukuza is shown is shown below for each 5 years.
\begin{tabular}{|l|l|l|l|l|l|}
\hline Year & 2016 & 2017 & 2018 & 2019 & 2020 \\
\hline Price & 17.8 & 29.6 & 41.1 & 46.3 & 46.5 \\
\hline
\end{tabular}
2.2.1 Find the percentage increase in the price of laundry detergent between each period.
2.2.2 Use the 4 percentages in question 2.2.1 above, to calculate the overall geometric mean percentage increase in the price of laundry detergent each year.
2.2.3 Interpret the geometric mean calculated in 2.2 .2 above.
2.2 A manager informs 2 employees, Annie and Caroline, that their performance will be rated according to categories with the percentage weightings shown in the Table below. The one who obtains the largest weighted mean score will be awarded a salary rise.
\begin{tabular}{|l|l|}
\hline Category & Weighting \\
\hline Initiative & \( 30 \% \) \\
\hline Creativity & \( 50 \% \) \\
\hline Ability to meet deadlines & \( 20 \% \) \\
\hline
\end{tabular}
Annie and Caroline are given score out of 10 in each category, and their scores are shown below.
\begin{tabular}{|l|l|l|}
\hline Category & Annie's scores & Caroline's scores \\
\hline Initiative & 3.5 & 6.0 \\
\hline Creativity & 8.0 & 6.5 \\
\hline Ability to meet deadlines & 5.5 & 8.0 \\
\hline
\end{tabular}
2.2.1 Calculate the unweighted mean score for each employee, state who get salary rise sing this method.
2.2.2 Calculate the weighted mean score for each employee, and state who get salary rise using this method
