central tendency and dispersion

• a measure of central tendency is a single value that summarises a set of data by identifying the typical value of the data set, also known as an average
• mode

  the most frequent score in a quantitative data set. If there are two modes, the data is bi-modal, and if there are more than two modes, the data is multi-modal
• strengths of the mode

  • The mode is not affected by extreme scores
  • It is much more useful for discrete data e.g. saying the average family has 2 children instead of 1.82
• weaknesses of the mode

  • It is not a useful method of describing data when there are several modes or no modes. this means that sometimes, the mode doesn't give an exact average value.
  • It tells us nothing about the other values in a distribution so it isn't as sensitive as the mean
• median


  the value in the central position of a data set
• median strengths

  • The median is not affected by extreme scores
  • It can be very easy to calculate
• median weaknesses

  • The median is not as sensitive as the mean because the exact values are not reflected in the final calculation
  • if there are an even amount of data points, the typical value will not be one of the recorded values
• mean


  the mathematical average, calculated by adding all the numbers and dividing by the number of values
• mean strengths

  • The mean is the most sensitive measure of central tendency because it takes account of ALL values within the data set
• mean weaknesses

  • The sensitivity of the mean means that it can be easily distorted by one (or a few) extreme values and end up being misrepresentative of the data as a whole
• a measure of dispersion is a single value that summarises the spread of a set of data
• range

  the range is the difference between a data set's highest and lowest values
• range strengths

  • easy to calculate compared to the other measure of dispersion, standard deviation
• range weaknesses

  • It is affected by extreme values
  • It fails to take into account the distribution of the numbers. For example, it doesn’t indicate whether most numbers are closely grouped around the mean or spread out evenly
• standard deviation

  a complex calculation that uses all data points to produce a single value. the smaller the standard deviation, the more clustered the values are around the mean
• standard deviation strengths

  • A precise measure of dispersion because it takes all the exact values into account
  • It is not difficult to calculate with a calculator
  • it provides information about the spread of scores
• standard deviation weaknesses

  • extreme scores distort the SD
  • the SD is significantly more difficult to calculate than the range
• Percentage: ‘Per cent’ means ‘out of 100’ (cent = 100)

  Thus, 5% essentially means 5 out of 100 or 5/100. The

  fraction has been converted to a percentage.
• We can also write 5/100 as a decimal = 0.05, because the first decimal place is out of 10 and the second is out of 100(0.5 would be 5 out of 10, not 5 out of 100).
• To change a fraction to a percentage, divide the numerator

  by the denominator. Then multiply by 100.
• In order to round to a given number of significant digits:

  1. Locate the significant figure for the degree of accuracy required. The first non-zero digit is the first significant figure.
  2. Look at the next digit to the right. Is it 5 or more?
  3. If it is 5 or more – round up by adding 1 to the previous digit.
  4. If it is less than 5 – round down by keeping the previous digit the same. If the degree of accuracy is 10 or more, fill in zeros to make the number the correct size.