Measures Of Location And Spread Flashcards
(20 cards)
What does the symbol ‘Ex’ represent?
The sum of all data values.
What does the symbol ‘x bar’ represent and look like?
Represents the mean of all data.
Looks like the letter ‘x’ with a horizontal line above it.
What does the letter ‘n’ represent?
The number of data values.
What does the symbol ‘Efx’ represent?
The sum of (the data values ✖️their frequencies)
What does the symbol ‘Ef’ represent?
The sum of the frequencies of the data values.
Name the 3 most basic measures of spread:
The range.
The interquartile range (IQR).
The inter-percentile range.
What 2 phrases can measure of spread sometimes be called?
Measures of dispersion.
Measures of variation.
Define the verb deviate (not in maths terms) and give 2 other words for deviate:
To depart from an established course.
Drift, turn away.
What is the most complicated measure to work out the spread of a data spread?
Variance
What does variance do?
Makes use of the fact that each data point deviates from the mean by the amount ‘x- bar x’
Formula for variance (both versions):
E(x-bar x)² ➗ n
= (Ex² ➗ n) - (Ex ➗ n)²
How are the units of variance and the units of data related?
Units of variance= (units of data)²
Give the symbol for standard deviation and variance:
Standard deviation - ‘o’
Variance - ‘o²’
Give the formula for standard deviation (both versions):
(E(x-bar x)² ➗ n)^1/2
= ((Ex² ➗ n) - (Ex ➗ n)² )^1/2
Note: For the ‘x²’ part, you square all x values then add them up.
Give the formula for standard deviation when including frequency (both versions):
(Ef(x - bar x)² ➗ Ef)^-2
= ((Efx² ➗ Ef) - (Efx ➗ Ef)²)^-2
Note: For the ‘x²’ part, you square all x values then add them up.
Formula you need to know for histograms:
Frequency= class width X frequency density
What are the 6 values used on an interpolation graph for frequency (name the positions of them)?
Top right: Upper class boundary. Top centre: The class you are trying to find (UQ,LQ/median/percentile etc…) Top left: Lower class boundary. Bottom right: Cumulative frequency of upper boundary of class. Bottom centre: Cumulative frequency of class you want to find. Bottom left: Cumulative frequency of lower boundary of class.
Formula for value you want to find (using abbreviated positions of interpolation graph):
(TC-TL)/(TR-TL) = (BC-BL)/(BR-BL)
If data is coded using formula ‘y=(x-a)/b’ , what would the formula for the mean of the coded data be?
Bar y = (bar x -a)/b
If data is coded using formula ‘y=(x-a)/b’ , what would the formula for the standard deviation of the coded data be?
O(y) = O(x) / b
