Measures of central tendency + dispersion Flashcards
What are the measures of central tendency?
The measures of central tendency are ‘averages’ which give us information about the most typical values in a set of data
How many types of measures of central tendency do you need to consider?
What are the names of the different measures of central tendency?
There are three types of measures of central tendency to consider;
- Mean
- Median
- Mode
What is the mean?
The mean is the average
How is the mean calculated?
The mean is calculated by adding up al. the score or values in a set of data and dividing this figure by the total numbers of scores there are
Work out the mean of these numbers:
5,7,7,9,10,11,12,14,15,17
Step 1:
5+7+7+9+10+11+12+14+15+17
Step 2:
107 is the total then divide by the total amount of numbers (10)
Step 3:
107 ÷ 10 = 10.7 (the mean)
What is a strength of the mean? (representative)
The mean is more representative of the data as it includes all of the scores/values in the data set within the calculation
What is a limitation of the mean? (reliability)
The mean can be easily distorted by extreme values, so does not have complete reliability
What is the median?
The median is the middle value in the data set when scores are arranged from lowest to highest
How is the median calculated?
When there is an odd number of values the median is easily identified
In a set of even numbered scores, the median is halfway between the two middle scores
What is a strength of the median? (unaffected values)
An advantage of using the median is that extreme scores do not affect the value, allowing the median to remain the same no matter how extreme the values. The median is also very easily calculated
What is a limitation of the median? (sensitivity)
The median is less sensitive than the mean because it does not include all the scores in the final calculation
How is the mode calculated?
The mode is calculated by placing the numbers in order and having the most common number identified
What is the mode?
The mode is the most frequently occurring score/value within a set of data
What are some anomalies that present themselves when calculating the mode?
In some data sets there may be two modes (bi - modal) or no mode if all the scores are different
What is a limitation of using the mode? (representation)
The mode is a very crude measure. It can be affected a change of one score and is sometimes not representative of the whole data
What is a strength of using the mode? (extreme value)
The mode result does not tend to be unaffected by extreme values
What are the measures of dispersion?
The measures of dispersion are the general term for any measure if the spread or variation in a set of scores
How many types of measures of dispersion do you need to consider?
What are the names of the different measures of dispersion?
There are two measures of dispersion to consider;
- Range
- Standard deviation
What is the range?
The range is the calculation used to work out the spread of scores by taking the lowest value from the highest value then adds one
What is the range of the following numbers:
0, 47, 49, 50, 50, 51, 53, 54, 56, 56, 57, 100
100 - 0 = 100
100 + 1 = 101
What is the strength of using the range? (minimum effort)
The range is quick to obtain as it is easy to calculate
What is a limitation of using the range? (representation)
The range only takes into consideration the two most extreme values, which may be unrepresentative of the data set as a whole
What is standard deviation?
Standard deviation is a single value that tells us how far scores deviate from the mean
As standard deviation grows, what does this show?
As standard deviation becomes larger, it shows a greater dispersion or spread of the set of data
What does a low standard deviation reflect?
A low standard deviation value reflects the fact that the data may be tightly clustered around the mean, which might imply that all participants responded in a fairly similar way
What is a strength of using the standard deviation? (precise measure)
The standard deviation is a much more precise measure of dispersion than the range as it includes all values within the final calculation
What is a limitation of using the standard deviation? (distortion)
The standard deviation tends to be distorted by a single extreme value
