19. Descriptive Statistics Flashcards
What do Descriptive statistics do
- Descriptive statistics simply describe the patterns found in a set of data.
- Descriptive statistics uses the term ‘central tendency’ to describe an average. For eg, the central tendency (average) for height of a group of 18yr old boys might be 1.70m.
3. Measures of dispersion describes how spread out the data is. For eg, the difference in height between shortest 18yr old boy & tallest might be 35cm.
What are the 3 measures of Central tendency
- Mean
- Mode
- Median
What is the Mean
- This is the ‘normal average’.
- Calculate by adding all the scores in a data set & then dividing by the no. of scores.
see pg114 for symbols & egs.
ADVANTAGES of calculating the Mean
- It uses all the scores in a data set.
- Its used in further calculations & so its useful to work it out.
DISADVANTAGES of calculating the Mean
- It can be skewed (distorted) by extremely high or low scores. This can make it unrepresentative of most of the scores, & so it may be misleading. In these cases, it’s best not to use the mean.
- It can sometimes give an unrealistically precise value (eg. the average family has 2.4 children, but what doesn’t 0.4 of a child mean..?)
What is the Mode
- The score that occurs most often.
see pg114 for eg
ADVANTAGES of calculating the Mode
- It shows the most common or ‘important’ score.
- It’s always a result from the actual data set, so it can be a more useful or realistic statistic, eg. the modal average family has 2 children, not 2.4.
DISADVANTAGES of calculating the Mode
- It’s not very useful if there are several modal values, or if the model value is only slightly more common than other scores.
- It has little further use in data analysis.
What is the Median
- The middle score when the data is put in order.
see pg115 for egs
ADVANTAGES of calculating the Median
- It’s relatively quick & easy to calculate.
- Its not affected by extremely high or low scores, so it can be used on ‘skewed’ sets of data to give a representative average score.
DISADVANTAGES of calculating the Median
- Not all the scores are used to work out the median.
- It has little further use in data analysis.
What do Measures of Dispersion tell you
Measures of Dispersion tell you how spread out the data is.
What is Range
Highest score minus the lowest score.
see pg115 for eg
ADVANTAGE of calculating the Range
- Its quick & easy to calculate.
DISADVANTAGE of calculating the Range
- It completely ignores the central values of a data set, so it can be misleading if there are very high or low scores.
(The IQR can be calculated to help AVOID this disadvantage)
How to calculate the IQR
Q3 - Q1
see pg115 for eg
What is Standard Deviation
SD measures, on average, how much scores deviate from the mean.
Equation for Standard Deviation
see pg 116 for equation + eg
What does a high Standard Deviation show
Shows more variability in a set of data.
ADVANTAGES of calculating Standard Deviation
- All scores in the set are taken into account, so it’s more accurate than the range.
- It can also be used in further analysis.
DISADVANTAGES of calculating Standard Deviation
- Its not as quick or easy to calculate as the range.
