Reading statistics and data as evidence

Overview

Checking a supplied table before quoting from it, why an absolute figure needs a base, per cent against percentage points, and how much weight a projection deserves.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What should you check about a supplied data table before you use any figure from it?

   Model answer

   The units, the dates covered, the source, the geographical area the figures refer to, whether they are raw counts or already processed into rates or percentages, and whether anything is missing. A figure quoted without its units or its year is uninterpretable, and figures for a district cannot be used to argue about a single village.

2. 2

   Why is an absolute figure often misleading unless you give it a base?

   Model answer

   Because size differences swallow the comparison. A town recording 300 unemployed people is not necessarily worse off than one recording 150 - it may simply be twice the size. Converting to a rate or percentage of the relevant population puts the places on the same footing. The same applies to a scheme creating 400 jobs: it means one thing in a city and something quite different in a rural district.

3. 3

   What is the difference between a rise of 5 per cent and a rise of 5 percentage points, and why does the confusion matter here?

   Model answer

   If unemployment rises from 8 per cent to 13 per cent, that is a rise of 5 percentage points but an increase of about 63 per cent on the original figure. Percentage change measures growth relative to the starting value; percentage points measure the arithmetic gap between two percentages. Mixing them up can make a modest change look dramatic or a serious one look trivial, and it undermines every conclusion built on it.

4. 4

   Why is it risky to judge an option on a single year's figure?

   Model answer

   Because one year may be an anomaly - an exceptional storm, a recession, a one-off closure - and choosing a different base year can reverse the apparent direction of change. Look for the trend across the whole series, note the range, and say if the series is too short to establish one. Where you only have one year, use it, but state that limitation rather than presenting it as a trend.

5. 5

   When should you prefer the median to the mean in data you have been given?

   Model answer

   When the distribution is skewed or contains extreme values, which is usual for house prices, incomes, farm sizes and flood damage costs. A few very large values pull the mean upwards so it no longer describes a typical case, while the median - the middle value when the data are ranked - is unaffected by them. Where both are supplied, a large gap between them is itself evidence of inequality worth commenting on.

6. 6

   What does looking at spread add to a comparison of two averages?

   Model answer

   It tells you whether the average is representative. Two areas can share a mean income while one is uniform and the other sharply divided, and the second raises questions of who would gain from a scheme. The range shows the gap between highest and lowest but is distorted by a single outlier; the interquartile range, covering the middle half of the ranked data, is more robust and gives a fairer picture of typical variation.

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