Measures of Central Tendency and Dispersion

• what is descriptive data?

  quantitative data that has been analysed to show patterns. helps to see the main trends in results.
• what are measures of central tendency?

  describes a set of data by identifying one score that represents the general trend of that data. this tends to be somewhere central to other scores.
• what are the strengths of mean?

  more sensitive than the median, because it makes use of all the values of the data.
• what are the weaknesses of mean?

  it can be misrepresentative if there is an extreme value.
• what are the strengths of median?

  it is not affected by extreme scores, so can give a representative value.
• what are the weaknesses of median?

  it is less sensitive than the mean, as it does not take into account all of the values.
• what are the strengths of mode?

  useful when the data is in categories, such as the no. of...
• what are the weaknesses of mode?

  not a useful way in describing data where there are several modes.
• the more sensitive?

  the less representative.
• what are measures of dispersion?

  • measures of 'spread'.
  • looks at how 'spread out' the data is.
  • are the scores similar to each other (close together), or quite spread out.
• what is range?

  what is happening at the end of each data set. (diff between the highest and lowest numbers).
• what is standard deviation?

  the avg distance of each score from the mean.
• what is high standard deviation?

  scores deviate a lot from the mean (spread out).
• what is low standard devation?

  scores don't deviate much from mean (not as spread out!).
• strengths of range?

  quick and easy to calculate.
• what are the weaknesses of range?

  • affected by extreme values (outliers).
  • does not take into account all the values.
• what are the strengths of standard deviation?

  more precise measure of dispersion because all values are taken into account.
• what are the weaknesses of standard deviation?

  much harder to calcuate than the range.
• what is normal distribution?

  a bell curve.

  
• how can we check whether data is normally distributed?

  • has the same, mean, median and mode.
  • symmetry about the centre.
  • 50% of values less than the mean and 50% of values greater than the mean.
• what is skewed distribution?

  tends to have a long tail on one side or the other.

  
• what is a negative skew?

  • long tail is on the negative side of the peak (skewed to the left).
  • mean is on the right of the peak value.
  • other central tendencies are lower than the mean.

  
• what is a positive skew?

  • long tail is on the positive side of the peak (skewed to the right).
  • mean is on the right side of the peak value.
  • other central tendencies are lower than the mean.