Summarising Data Flashcards
What is an average
A single value used to describe a data set
It is a measure of central tendency
The mode median and mean are averages
What is the mode
The value which is most often
What is the median
The middle value
When the number of the data sets values are odd how do you find the median
It is the 1/2(n+1) observation
Where n is the number of values
How do you calculate the mean
Sum of x(÷n)
What is the mode in classed frequency data
The category / class with the highest frequency
How do you find the median category in frequency table data
It is the class that contains the 1/2(n+1)th value
What is the modal class
The class with the highest frequency
How do you find the median for continuous data
It is the 1/2nth value
What is linear interpolation
A method used to estimate the median value in grouped data
How do you find the median / a quartile using linear interpolation
Find where the median is in the grouped data. This is done by finding the position, and then using cumulative frequency to see which group it is in.
Find out how far into the group your median is in
Then use the formula
(Median value - cumulative frequency before ÷ change in cumulative frequency) × class width
Basically what you are doing finding how far into the group your value is, finding this in proportion to the values in your group and multiplying by the class width
How do you calculate an estimated mean from grouped data
Sum of (f×midpoint) ÷ sum of f
What happens to the averages when you increase / decreases by a set percentage
The averages increase or decrease for a set percentage
Why do we transform data
To make it easier to calculate the mean
How do you transform data with decimals
Subtract each decimal from the same integer
Then multiply them until they are whole numbers
Now calculate your average
Then reverse the calculations you did to find a mean (divide by your multiple of 10 and add your number)
What is a geometric mean
An average that multiplies all the values and roots the number
It is more accurate and effective than using an arethmatic mean
How do we calculate geometric mean
n√v¹×v²×v³ etc…
N is the number of values
The values are rooted by n
Why are weighted means used
For data with different values or weightings in each group
How are weighted means calculated
Sum of (value × weight) ÷ sum of weights
(Total wx) ÷ total w
What is a range
Largest value - smallest value
What is an interquartile range
Upper quartile - lower quartile
What are the upper and lower quartiles
Upper = 3/4 th value
Lower = 1/4 th value
How do you calculate quartiles in discrete data
The same ways as means but using the quartiles as a fraction rather than 1/2
E.g 1/4(n+1)
How do you calculate the range in a frequency table
Take the largest possible value and smallest possible value from the table
Subtract these values
