Y1, C2 - Measures of Location & Spread Flashcards
What are measures of location
Single values which describe a position in a data set
What are measures of spread to do with and give examples
How data is spread out
e.g. range, variance, IQ range, standard deviation
What are the measures of central tendency
Mode
Median
Mean
What does x bar mean
The mean value of x
What is the formula for the mean of ungrouped data
(Sum of the values * frequencies) / (sum of the frequencies)
What is the formula for the mean of grouped data
Find the midpoint of each group and assign to x (assume all values are the midpoint value)
(Sum of the values * frequencies) / (sum of the frequencies)
What type of data can’t a calculator find the IQ ranges for
Grouped data
What does the median ignore
Extreme values
What is the median
The middle value of data
How to find the median of ungrouped data
n / 2
Where n is the number of items
If a decimal, round up
If a whole number, half way between this item and the one after
How to find the median of grouped data
n / 2
Use linear interpolation
What is the class width of: Weight of cat to the nearest kg 10 - 12
3
9.5 <= w < 12.5
How to find upper and lower quartiles
1n/4 or 3n/4
Where n is the number of items
If a decimal, round up
If a whole number, half way between this item and the one after
Notation for quartiles, median, deciles and percentiles
Q1
M / Q2
D3 / P30
P25 / Q1
How to calculate IQ range
Q3 - Q1
What is the variance
A measure of spread which takes all values into account
The average squared distance from the mean
Formula for variance of ungrouped data
Sum of squared distance from the mean / number of values
OR
(Sum of the values squared / number of values) - mean squared
What is standard deviation
The square root of variance
What is the average distance from the mean called
The standard deviation
What parts of coding affect measures of spread
Only multiplicative parts
Which parts of coding affect measures of location
All parts of coding
What is the formula for linear interpolation to find the median of cumulative data
Median = start value + (fraction from top) x class width)
Where if the frequency was 55 to 100 and you were finding the 75th position, the fraction from top would be 20 / 45
