Range and Outliers: How One Late Delivery Changes the Measures

0:00How much can one extreme value change a summary of data?

0:05A shop records seven delivery times, in minutes: 22, 25, 25, 27, 28, 30 and 31.

0:16The range is the largest value minus the smallest, a measure of spread: 31 minus 22 is 9.

0:26The mean and the median are measures of central tendency: each gives a typical value.

0:32The mean is the total divided by the number of values: 188 divided by 7 is about 26.9.

0:42The median is the middle value in order. With seven values, it is the fourth: 27.

0:50Now add one late delivery of 95 minutes.

0:54A value far from the rest of the data is called an outlier.

0:59The range jumps to 73, because 95 minus 22 is 73.

1:06The mean is now 283 divided by 8, about 35.4, more than seven of the eight times.

1:15With eight values, the median is halfway between 27 and 28, which is 27.5.

1:23One value moved the range by 64 and the mean by about 8.5, but the median by only half a minute.

1:32Should we remove the 95? First, ask why it is there.

1:37If it is a mistake in the record, such as a typing error, correct it or leave it out.

1:43If it is a real delay, keep it: the shop needs to know about it.

1:49A common mistake is deleting every outlier without asking why it is there.

1:54Recap: one outlier can stretch the range and pull the mean, while the median barely moves.