Question

William Sealy Gosset worked at the Guinness Brewery in Dublin and made substantial contributions to the practice of statistics. In his work at the brewery, he collected and analyzed a great deal of data. Archives with Gosset’s handwritten tables, graphs, and notes have been preserved at the Guinness Storehouse in Dublin. In one study, Gosset examined the change in the double stout market before and after World War I (1914‑1918). For various regions in England and Scotland, he calculated the ratio of sales in 1925, after the war, as a percent of sales in 1913, before the war. Here are the data:

Region Ratio
Bristol 94
Cardiff 112
English Agents 78
English O 68
English P 46
English R 111
Glasgow 66
Liverpool 140
London 428
Manchester 190
Newcastle‑on‑Tyne 118
Scottish 24

(a) Compute the mean for these data. Give your answer to two decimal places.
⎯⎯⎯=
(b) Compute the median for these data. Give your answer to two decimal places.
=
(c) Which measure describes the center of this distribution the most accurately? Explain your answer.

The mean represents the center of the data most accurately because the mean incorporates all of the individual values, whereas the median depends more on the order of the values than their actual amounts.

The mean and the median should both be used. By comparing the mean and median, you can tell if the data are skewed.

The median represents the center of the data most accurately because the mean is more affected by extreme values.

The mean and the median are equally as accurate because the distribution of the data is approximately symmetical.
Region RelativeTo1913 RelativeToPast4
Bristol 94 82
Cardiff 112 80
English Agents 78 83
English O 68 88
English P 46 99
English R 111 99
Glasgow 66 78
Liverpool 140 106
London 428 105
Manchester 190 107
Newcastle-on-Tyne 118 115
Scottish 24 78

Answer 1

Answer: a) To compute the mean of these data, we need to add up all of the ratios and divide by the total number of ratios.

(94+112+78+68+46+111+66+140+428+190+118)/11 = 101.36

The mean is 101.36

b) To compute the median of these data, we need to arrange the data in increasing order and find the middle value.

46, 66, 68, 78, 94, 111, 112, 118, 140, 190, 428

The median is 111

c) The measure that describes the center of this distribution the most accurately is the mean, because it takes into account all of the values in the data set and provides an overall measure of central tendency. The median is also a measure of central tendency but it is affected by the outliers present in the dataset and doesn't provide a good representation of the central value.

Explanation: