Measures of Central Tendancy Flashcards
What are the 3 measures of central tendency?
- Mode
- Mean
- Median
What does bimodal mean?
A data set in which 2 modes can be identified
What does multi modal mean?
A data set in which two or more modes can be identified
What is the mode?
The data value that occurs most frequently in the set
How is mode calculated?
Put the raw data in order so that values which are the same will appear together in the list
What is frequency distribution?
A table that shows the frequency with which each value occurs in a data set
What is grouped frequency distribution?
A table in which the values are formed into groups and the number of occurrences in each group from a data set is recorded.
Which data type is more appropriate for using the mode?
The mode is a suitable measure of central tendency when the data are QUALITATIVE Mode can be used for quantitative data as well but it is not very informative when a data set is multimodal or has no mode at all
What is mean?
The average of all the data in the set
How do you calculate the mean?
Sum of data values / No. values in the set
What is the equation of the mean for a raw data set?
What is the equation for the mean if the data is summarised in a grouped frequency distribution?
How do you work out the mean when the data is summarised in a grouped frequency distribution?
Use the frequency distribution formula where each value of x is represented by the class mid-point
What type of data is the mean suitable for?
Discrete or continuous quantitative data
It is not suitable for qualitative data set which does not contain numerical values
Why is the mean the most popular measure of central tendancy?
The calculation uses all of the data values and is therefore truly representative of the whole set
What is the problem with using the mean?
It can be highly influenced by extreme values
What is the median?
The middle point when the data set is ordered
The middle value which divides a set of ordered data into 2 halves
How is the median found when n is an odd number and a single middle value exists (raw data and frequency distribution)?
1/2(n+1)
How is the median found when n is an even number (raw data and frequency distribution)?
Identify the two values closest to the middle and find their average
Their positions found in an ordered set of data are found using : 1/2n and 1/2n+1
E.g. there are 6 customers in the queue for till 14, so the position of the two values closest to the middle are found usinfg 1/2(6) and 1/2(6)+1 which identifies the amount of money spent by the 3rd and 4th customers
What formula do we apply when trying to find the median for grouped frequency distribution?
- b = lower case boundary
- f = the sum of all frequencies that occur before the median class
- fm = the frequency of the median class
- w = the class width of the median class
What are the advantages of using mode?
- Always easy to understand and calculate
- Can be used for both quantitative and qualitative data
- Unaffected by extreme values
- Always is one of the data values in the set
What are the advantages of using mean?
- Mostly easy to understand and calculate
- Uses all of the data values in the set
- Provides a single response
What are the advantages of using median?
- Provides a single result
- Is sometimes one of the data values in the set
