Measures of Central Tendencies for Ungrouped Data
Mean, Mode, Median, and Range
Sure, the words "Mean, Median, Mode and Range" all sound confusing··· But what about the words we already know,
like "Average, Middle, Most Frequent, and Difference"?
They are all the same ideas!
Definition: What is the Mean?
The SUM of the data, divided by the number of items in the set of data··· commonly called
Definition: What is the Median?
The middle number in the set of data when written "in order"
Definition: What is the mode?
The data item that appears the "MOST"
Definition: What is the range?
It is a measure of dispersion that calculates the difference between the largest and smallest number in a set.
The prices, in dollars, of the cars sold by a car salesperson in one week are shown below:
4300, 5400, 3200, 6200, 5400, 5500, 6400
Question:Find the mean, median, mode and range
Answers: Mean= 4314.3; Median = 5400; Mode = 5400; Range = 6400 - 3200 = 3200
Definition: Variance is defined as the average of the square deviations as shown below:
What Does the Variance Formula Mean?
- Variance is the mean of the squared deviation scores.
- The larger the variance is, the more the scores deviate.
- On average, away from the mean. The smaller the variance is, the less the scores deviate, on average, from the mean.
The standard deviation is the square root of variance.
Variance = standard deviation2.
When calculating variance, it is often easier to use a computational formula which is algebraically equivalent to the definitional formula:
An example is illstrated below:
Now, it is time to answer simple questions then check your answers with the provided solutions.
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Date of last modification: March 5, 2019