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Shara

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Chapter 3 – Representation and summary of data Test

1.) A travel agent sells holidays from his shop. The price, in £, of 15 holidays sold on a particular day are shown below.
|299 |1050 |2315 |999 |485 |
|350 |169 |1015 |650 |830 |
|99 |2100 |689 |550 |475 |

For these data, find

(a) the mean and the standard deviation,
(3)

(b) the median and the inter-quartile range.
(4)

An outlier is an observation that falls either more than 1.5 × (inter-quartile range) above the upper quartile or more than 1.5 × (inter-quartile range) below the lower quartile.

(c) Determine if any of the prices are outliers.
(3)

The travel agent also sells holidays from a website on the Internet. On the same day, he recorded the price, £x, of each of 20 holidays sold on the website. The cheapest holiday sold was £98, the most expensive was £2400 and the quartiles of these data were £305, £1379 and £1805. There were no outliers.

(d) On graph paper, and using the same scale, draw box plots for the holidays sold in the shop and the holidays sold on the website.
(4)

(e) Compare and contrast sales from the shop and sales from the website.
(2)
(Total 16 marks)
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2.) Cotinine is a chemical that is made by the body from nicotine which is found in cigarette smoke. A doctor tested the blood of 12 patients, who claimed to smoke a packet of cigarettes a day, for cotinine. The results, in appropriate units, are shown below.

|Patient |A |B |C |D |E |F |G |H |I |
|17, |16, |15, |14, |16, |17, |15, |25, |18, |16 |

(a) Find the median and inter-quartile range of the waiting times. (5) An outlier is an observation that falls either 1.5 ( (inter-quartile range) above the upper quartile or 1.5 ( (inter-quartile range) below the lower quartile.

(b) Draw a boxplot to represent these data, clearly indicating any outliers.
(7)
(c) Find the mean of these data.

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