Research Methods- Data analysis: Descriptive statistics Flashcards
Descriptive statistics -
The use of graphs, tables and summary statistics to identify trends and analyse sets of data.
Measures of central tendency -
The general term for any measure of the average value in a set of data.
Mean -
The arithmetic average calculated by adding up all the values in a set of data and dividing by the number of values there are.
Median -
The central value in a set of data when values are arranged from lowest to highest.
Mode -
The most frequently occurring value in a set of data.
What are measures of central tendency?
Measures of central tendency are averages that provide information about the most typical values in a dataset. The three main measures are the mean, median, and mode.
What is the mean?
The mean is the arithmetic average, calculated by adding all scores in a dataset and dividing by the total number of scores.
How is the mean calculated?
For the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the mean is calculated as (5+7+7+9+10+11+12+14+15+17) ÷ 10 = 10.7.
What is a strength of the mean?
It is the most sensitive measure of central tendency as it includes all scores in the dataset, making it representative of the data as a whole.
What is a limitation of the mean?
It can be easily distorted by extreme values. For example, replacing 17 with 98 changes the mean to 18.8, which is not representative of the dataset.
What is the median?
The median is the middle value in a dataset when scores are arranged in order.
How is the median calculated?
For an even number of scores, the median is the average of the two middle values. In the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the median is (10 + 11) ÷ 2 = 10.5.
What is a strength of the median?
It is not affected by extreme values, making it more reliable for datasets with outliers.
What is a limitation of the median?
It is less sensitive than the mean because it does not include all scores in the calculation.
What is the mode?
The mode is the most frequently occurring value in a dataset.
What is an example of the mode?
In the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the mode is 7.
What is a limitation of the mode?
It is a crude measure and may not be representative of the dataset as a whole.
What is a strength of the mode?
It is easy to calculate and is the only measure of central tendency that can be used for categorical data.
What is a bimodal dataset?
A bimodal dataset has two modes, meaning two values occur with the same highest frequency.
What are measures of dispersion?
Measures of dispersion describe how spread out the scores in a dataset are. The two main measures are the range and standard deviation.
What is the range?
The range is the difference between the highest and lowest values in a dataset, often calculated as (highest value - lowest value) + 1.
How is the range calculated?
For the dataset: 5, 7, 7, 9, 10, 11, 12, 14, 15, 17, the range is (17 - 5) + 1 = 13.
What is a strength of the range?
It is easy to calculate and provides a quick measure of spread.
What is a limitation of the range?
It only considers the two extreme values, which may not represent the overall spread of the dataset.
What is standard deviation?
Standard deviation is a measure of how far scores deviate from the mean, providing a precise measure of dispersion.
What does a high standard deviation indicate?
A high standard deviation indicates that scores are widely spread, suggesting variability in responses or effects.
What does a low standard deviation indicate?
A low standard deviation indicates that scores are tightly clustered around the mean, suggesting consistency in responses or effects.
What is a strength of standard deviation?
It includes all values in the calculation, providing a precise measure of dispersion.
What is a limitation of standard deviation?
It can be distorted by extreme values, similar to the mean.
What is an example of a dataset with a misleading range?
In the dataset: 0, 47, 49, 50, 50, 50, 51, 53, 54, 56, 56, 57, 100, the range is 101, but most scores are clustered around 50, making the range unrepresentative.
What is the purpose of adding 1 to the range?
Adding 1 accounts for rounding errors in raw scores, ensuring the range accurately reflects the spread of data.
What is the relationship between standard deviation and the mean?
Standard deviation measures how far scores deviate from the mean, providing insight into the variability of the dataset.
What is an example of a dataset with a low standard deviation?
A dataset with scores: 10, 11, 12, 11, 10 has a low standard deviation, indicating scores are close to the mean.
What is an example of a dataset with a high standard deviation?
A dataset with scores: 5, 20, 35, 50, 65 has a high standard deviation, indicating scores are widely spread.
What is the importance of measures of central tendency?
They provide a summary of the most typical or central values in a dataset, helping researchers understand the overall pattern of data.
What is the importance of measures of dispersion?
They describe the spread or variability of scores, providing insight into the consistency or variability of responses in a dataset.
What is the difference between the mean and the median?
The mean is the arithmetic average, while the median is the middle value. The mean is sensitive to extreme values, whereas the median is not.
What is the difference between the range and standard deviation?
The range is a simple measure of spread based on extreme values, while standard deviation is a precise measure of how far scores deviate from the mean.
What is the role of the mode in categorical data?
The mode is the only measure of central tendency that can be used for categorical data, identifying the most frequently occurring category.
What is an example of a dataset with no mode?
A dataset with scores: 5, 7, 9, 11, 13 has no mode, as all values occur with the same frequency.
What is the significance of standard deviation in experiments?
A high standard deviation suggests variability in responses to the independent variable, while a low standard deviation indicates consistent effects.
What is the impact of outliers on the mean and median?
Outliers significantly affect the mean but have little to no effect on the median, making the median more robust for datasets with extreme values.
