The mass $x$ grams of each of $90$ oranges of variety $A$ were recorded. The data obtained was

Question

The mass $x$ grams of each of $90$ oranges of variety $A$ were recorded. The data obtained was illustrated as shown in the table. Mass $x$ gramsNo. of oranges $60 < x \le 70$$1$ $70 < x \le 80$$3$ $80 < x \le 90$$9$ $90 < x \le 100$$28$ $100 < x \le 110$$37$ $110 < x \le 120$$8$ $120 < x \le 130$$4$ Find the mean and standard deviation for the above data. In an another variety, variety $B$, of the $90$ oranges, the lightest orange has the mass $55$ grams and the heaviest orange has the mass $138$ grams. The median, lower quartile and upper quartile are $102$ grams, $93$ grams and $109$ grams respectively. Draw the box-whisker diagram for this data. If you were to buy some oranges, which variety would you buy? Explain your answer.

Accepted Answer

(a) mean $100$ g, standard deviation $11.1$ g (b) $55,93,102,109,138$ (c) Variety A (more consistent)

Mass \(x\) grams	No. of oranges
\(60 < x \le 70\)	\(1\)
\(70 < x \le 80\)	\(3\)
\(80 < x \le 90\)	\(9\)
\(90 < x \le 100\)	\(28\)
\(100 < x \le 110\)	\(37\)
\(110 < x \le 120\)	\(8\)
\(120 < x \le 130\)	\(4\)

Statistics - Mean and Standard Deviation for Grouped Data

Statistics - Mean and Standard Deviation for Grouped Data

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