Typical or most popular?

The idea

When a typical observation is wanted and extreme values may be present, the median is more appropriate than the mean; when the most frequent value or most popular item is wanted, the mode is the best choice.

A new worker asks

A new worker asks: "What does a typical worker earn here?" The workers earn 20, 25, 25, 30, 30, 35, 35, 40 (₹ thousand a month), and the owner earns 40 now, but may earn far more.

You could quote the mean or the median, the middle value.

Which would you quote if the owner's pay goes up to 100?

• The mean
• The median
• Both are equally good

Mean against median

Raise the owner's pay to 100, in steps of 5. The blue pivot is the mean. The green marker under the beam is the median. Which one moves?

Median or mode?

When a typical observation is wanted and extreme values may be present, the median is more appropriate than the mean. When the most frequent value or the most popular item is wanted, the mode is the best choice.

Median: the typical productivity of workers, the average wage in a country. Mode: the most popular TV programme, the consumer item in greatest demand, the colour of vehicle used by most people.

Notes

Median for a typical value when extreme values may be present. Mode for the most frequent value or most popular item.

Check yourself

We want the average wage in a country. A few people earn huge amounts. Which measure is more appropriate?

A shop wants to know which shirt size to stock the most. Which measure should it use?

With the owner at 100, the nine pays in order are 20, 25, 25, 30, 30, 35, 35, 40, 100. What is the median?

Answer: 30

The 5th value in the ordered list is 30. Four values are below it and four above it, and the owner's 100 did not change that.

Which measure is the best choice to find the most popular TV programme?

• The median — correct. Yes! The median is not pulled by a few huge wages, so it shows a typical wage.
• The mean. The huge wages would pull the mean up, as the owner's pay did.
• The mode. The mode gives the most common wage, not the typical wage.
• The mode — correct. Yes! The most frequently bought size is the most popular item, and the mode finds it.
• The mean. A mean size such as 38.6 may not be a size anyone wears.
• The median. The median is the middle size, not the one most people buy.
• The mode — correct. Yes! The mode is the most frequent value, the programme watched the most.
• The mean. You cannot average the names of programmes.
• The median. The median is the middle value, not the most popular one.