Whether large or small, any business needs accurate information, and an important source of information is statistical analysis. Accurate statistics can help a business know what is happening within the enterprise and guide future decision-making. However, statistics can easily mislead analysts while they are trying to interpret them. Using an adjusted mean can give a more accurate picture of the true situation.

Imagine that twenty people buy clothes in a store; the store owner wants to know the mean amount that each customer spends. The twenty customers spent the following amounts:

• Nine people spent \$90 each.
• Three people spent \$100 each.
• Six people spent \$105 each.
• One person spent just \$2 on a pair of socks.
• One person spent \$5000 on a complete wardrobe for the new season.

The customers spent a total of \$6742, this figure, divided by twenty, gives a mean spend of \$337.10. You would be correct if you thought that this figure does not reflect what people really spent because no one spent anything near \$337.10. Two amounts within the twenty do not reflect normal spending behavior: the woman who spent \$2 on a pair of socks and the man who spent \$5000 on a range of new outfits.

Using an adjusted mean, you exclude these two outliers and calculate a new figure: you now have a total of \$1740 which, divided by eighteen gives a total spend of \$96.67 which, although no one spent exactly this sum, gives a much more accurate figure.

Samantha is the owner of a bakery that supplies cakes and pastries to several local restaurants and stores. Samantha's bakery sells a range of low-calorie products that sold very well last month, and she wonders whether she should focus more on items of this type. Her sales last month break down as follows:

• Days 1 - 7: 670 'ordinary' cakes, 225 low-calorie cakes.
• Days 8 - 14: 630 'ordinary,' 187 low-calorie.
• Days 15 - 21: 642 'ordinary,' 845 low-calorie.
• Days 22 - 28: 663 'ordinary,' 212 low-calorie.
• Days 29-31: 189 'ordinary,' 121 low-calorie.

Samantha can see immediately that her 'ordinary' range of cakes outsold her low-calorie range, but those low-calorie items sold very well in the third week. This increase in sales is explained by the fact that there was a conference for fitness instructors during that week, and the instructors tended to opt for low-calorie desserts. Therefore, Samantha should consider the number of low-calorie cakes she sold during that week as an outlier and not indicative of a trend. She decides not to focus on low-calorie items.

An adjusted mean gives a clearer picture of the true situation by disregarding the influence of anomalous events. In simple situations, such as the ones given above, you can easily see the unusual figures. When there are more variables, however, an analyst will find it more difficult to find the outliers.