Summary Statistics Flashcards
Define central tendency.
The point at which the distribution is in balance (the middle).
List characteristics of the mean.
- Takes into account all values
- Central estimate
- Easily distorted by extreme values
When is the mean the preferred measure of central tendency?
When there are no extreme values.
What is the formula for the mean?
x! = ∑ x / n
x! = mean
∑ x = the sum of all observations
n = the number of observations in the sample
What is the median?
The exact middle value.
List characteristics of the median.
- Half of the values are smaller than the median and half are larger
- The median divides the distribution in two equal parts
What is the formula for the median?
Median = (n + 1)th / 2
What is the measure of dispersion?
Describes how the data is clustered or dispersed around
the mean.
What is the measure of variation?
Determines the range of the distribution relative to
the measures of central tendency.
What is the formula for the lower quartile?
Q1 = (n+1)/4 value of ordered observations
Q1 = The number below which lies the 25% of the bottom data
What is the formula for the upper quartile?
Q3 = 3*(n+1)/4 value of ordered observations
Q3 = It has 75% of the data below it & the top 25% of the data above it
What is the variance?
The deviations of the observations from the mean.
List characteristics of the variance.
- Measures the spread about the mean
- Measures ‘somewhat’ the average distance between to observation and mean value
- We need to calculate this in order to get the standard deviation
Write the formula for variance.
variance (s.d. squared) = ∑ (x − x!) squared / n -1
What does a low value of variance mean?
Data are clustered about the mean.
