Section 2 (Pgs 20-25) Flashcards
What are the 3 most common measures of central tendency?
Mean
Median
Mode
Most common measures of spread or variability? (4)
Standard deviation
Variance
Range
Semi-interquartile range
Symbol for mean of population?
µ (mu)
Symbol for standard deviation of population?
σ (sigma)
Symbol for mean of a sample?
x̅ (ex bar)
Symbol for standard deviation of a sample?
s
What is the mean?
The sum of data values divided by the number of data values
How do you calculate the mean from a frequency table?
Sum of frequencies multiplied by the midpoint of the group divided by total number of observations
How would you describe the sample mean as an estimator of the population mean?
Why?
Unbiased estimator
The mean of all possible sample means than can be selected from a population is equal to the population mean
Why is the mean an efficient summary statistic?
It uses all the data
What is a negative point about using the mean?
It is sensitive to extreme values so would not be used to summarise data with extreme values
What is the median?
The middle value when the data is ranked in numerical order
If the mean and median are the same, what does this say about the data?
The distribution is symmetrical and there are no extreme values
When is the median more appropriate to use than the mean as a measure of central tendency?
When there are extreme values
Is the median affected by extreme values?
No
What is the mode?
The most frequently occurring value in a data set
What is the mode useful for?
It is the only measure of centre for qualitative data
Is the mode sensitive to extreme values?
No, however it is wasteful of the data as it only uses one observation
When is the mean used?
As the measure of centre for quantitative data, unless the distribution of the data is skewed
When is the median used?
As the measure of centre for qualitative data when the distribution of the data is skewed/ there are extreme values
When is the mode used?
As the measure of the centre for qualitative data
What does the variance and standard deviation measure?
The spread of the data above the mean
How is the standard deviation related to the variance?
It is the square root of the variance
What is the variance?
The average of the squared deviations for the mean
How do you calculate the variance from a frequency table?
Sum of frequencies multiplied by midpoint - mean squared, divided by n -> same as variance equation with f before bracket
How would you describe the use of sample variance to estimate the population value?
Biased
Average of all sample variances is not equal to the population value
What does the population variance equal, in terms of the sample variance?
Sample variance X n/ n-1
How can the variance equation be changed to ensure that the sample variance provides an unbiased estimate of the population value?
n-1 is used as the denominator
How does the standard deviation relate to the spread of data?
The larger the standard deviation, the wider the spread of the data
If the standard deviation = 1, how many standard deviations would you expect 95% of the data to lie within?
2
What would a standard deviation of 0 mean?
There is no variation in the data -> all data is the same
What is the range a measure of?
The extremes (not the variability) -> not used very often as a measure of spread
What is the inter-quartile range?
The difference between the first and third quartiles
Is the inter-quartile range affected by extreme values?
No (it only includes the middle 50% of observations)
What is the most commonly used measure of spread of data about the mean for continuous data and most discrete observations?
Standard deviation
What is used preferentially to the standard deviation when there are outlying observations?
Inter-quartile range
What is the word used to describe data that is not symmetrical?
Skewed
What is it called when most values lie towards the bottom of the range and there is a tail to the right?
Positively skewed
What is it called when most values lie towards the top fo the range and there is a tail to the left?
Negatively skewed
Are positively or negatively skewed data more common?
Positively - negatively skewed data is rare
What does the coefficient of skewness do?
Indicates if the data is symmetrical or positively or negatively skewed
What does the coefficient of skewness equal if the data is symmetrical?
0
What does a coefficient of skewness greater than 0 indicate?
Positive skewness
What does a coefficient of skewness less than 0 indicate?
Negative skewness
What is kurtosis?
A measure of the peakedness of a distribution
What does a value of 0 for the kurtosis indicate?
A shape close to the normal distribution
What does a positive value for the kurtosis indicate?
A relatively peaked distribution
