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Which summary describes the centre or spread of these data?
More, if you want it
What does the researcher want to say about the patients' waiting times?Tap a term: its definition, what you can do with it, and how often the exam asks it.
Definition: the middle value once the values are put in order.
You can: Tell the median from the mean by whether one extreme value is present.
Definition: the largest value minus the smallest value.
You can: Tell the range from the interquartile range by whether only the largest and smallest values are used.
Definition: the non-parametric spread measure used for skewed data.
You can: Tell the range from the interquartile range by whether only the largest and smallest values are used.
Definition: the spread of raw data around the mean, equal to the square root of the variance.
Definition: the spread of raw data around the mean, before the square root is taken.
Each card is one term. The grey line is what the patient says, which is what the question stem gives.
Summary
The median is the middle value found by ordering the values from smallest to largest.
The median is the middle value found by ordering the values from smallest to largest. A set with an even number of values has two middle values. Taking the average of those two middle values gives the median of an even set.
Isla MacLeod is a research assistant in a psychology research office in Glasgow. Isla orders four clinic waits as 2, 3, 5 and 5 weeks. Isla says, "The two middle waits are 3 and 5, so the median is 4."
The mean is the sum of the values divided by their number. One very long wait pulls the mean upward. The median depends on position in the order, so one extreme value barely moves the median, unlike the mean. Skewed data need the median as their .
One textbook reports schizophrenia prevalence and morbid risk as medians, because those data are skewed. The means in those data come out higher than the medians. A few extreme values pull the mean upward. The median stays near the typical value.
Analogy
The waiting times are people standing in a queue, from shortest wait to longest wait. The median is the person in the middle of the queue. One person who waited far longer joins the back and leaves the middle person unchanged. The range is the gap between the front person and the back person.
Where the analogy breaks: with an even number of people, nobody stands exactly in the middle, so the two nearest are averaged.
4 more sections on Median, range, interquartile range, standard deviation and variance
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