Statistics Chapter 2 Flashcards
What is a measure of location?
A single value describing a position in a data set
What is a measure of central tendency?
A single value describing the centre of a data set
What is the mode/modal class?
The most often occurring value or class
What is the median?
The middle value of an ordered set of data
What is the mean?
The sum of the data values divided by the number of data values
x bar = sum of x / n
When should the mode be used? (2)
Qualitative data
Quantitative data with repeating values
What is a data set with two modes called?
Bimodal
When should the median be used?
Quantitative data; especially data with extreme values and outliers as they do not affect the average
When should the mean be used?
Quantitative data as it uses all values in order to give a true measure; not suitable when there are extreme values as this has a big effect on the average
What is the four pots method used for?
Finding quantiles for discrete data
How does the four pots method work? (3)
Divide the number of pieces of data by four
Place the data values as equally as possible into the four pots
Add remainders as evenly as possible in the spaces between the pots
What is linear interpolation used for?
Finding quartiles for continuous data
What is a measure of spread?
A measure of how spread out the data is
What is the range? (2)
The difference between the largest and smallest data values
Affected by extreme values
What is the interquartile range? (2)
Difference between quartile 1 and quartile 3
Not affected by extreme values but only considers middle 50%
What is the interpercentile range? (2)
Difference between two given percentiles
Often uses 10% and 90% as this gives a measure from 80% of the data but discounts extreme values
What is variance?
Works out the spread of the data
How is variance calculated? (2)
(Sum of x^2 / n) - (x bar)^2
Sxx / n
What is standard deviation? (2)
The higher the number the more spread out the data is
Always positive
How is standard deviation calculated?
✔️(sum of x^2 / n) - (x bar)^2
How is the standard deviation of grouped data calculated? (2)
✔️(sum of fx^2 / sum of f) - (sum of fx / sum of f)^2
Where x = midpoints of each group
What is coding?
A set of data values can be modified by using a formula:
y = (x - a) / b
How is the mean of coded data converted to the mean of the original data? (2)
(y bar) = (x bar) - a / b
Mean is affected by all transformations so it must be divided and subtracted from
How is the standard deviation of coded data converted to the standard deviation of the original data? (2)
(sigma y) = (sigma x) / b
As standard deviation is a measure of spread, adding or subtracting has no effect
