Descriptive Statistics

• Descriptive statistics are analyses of quantitative, numerical data that summarise patterns.
• Measures of central tendency are examples of descriptive statistics that depict an overall central trend in a set of data.
• The mean, median and mode are examples of measures of central tendency.
• The mode is the most frequently occurring number in a data set.
• The median is the middle score when the data are in numerical order.
• If there are an even number of scores when calculating the median, then take the sum of the two middle numbers and divide by two.
• The mean is the sum of all numbers in the data set, divided by how many numbers there are in the data set. This is also known as the average score.
• The median is calculated by arranging the data in ascending order and finding the middle value. If there is an even number of values, the median is the average of the two middle values.
• The mean is calculated by summing up all the values in a dataset and dividing by the total number of values.
• The purpose of measures of central tendency in descriptive statistics is to summarise and describe the typical or central value of a dataset.
• The mean takes all numbers of a data set into account (strength), but this also means that it is susceptible to skewing if the data features extreme values (weakness).
• The mode is of little use when the data set includes many different values of the same frequency, i.e. there are many modes.
• The mean is a good measure, as all the scores are taken into consideration, so it is highly representative of the whole data set.
• The mode in descriptive statistics is calculated by finding the value or values that occur most frequently in a dataset.
• To calculate the variance in descriptive statistics, you subtract the mean from each data point, square the result, sum up all the squared differences, and divide by the total number of data points.
• The range and standard deviation are measures of dispersion (spread of scores/ variation).
• The standard deviation is calculated by taking the square root of the variance.
• The range is calculated by taking the lowest score away from the highest score.
• The standard deviation tells us the spread of scores away from the mean (a high s.d. suggests more variation in the set of scores).
• A small standard deviation value suggests that most scores are close to the mean (average) score.
• A large standard deviation value suggests that most scores are spread out from the mean score (more variation).
• The standard deviation informs us about the spread of scores in a dataset by measuring the average distance between each data point and the mean of the dataset.
• Percentages are a way of summarising nominal level data (frequencies in categories). A percentage is a portion of a whole expressed as a number between 0 and 100 (instead of as a fraction).
• To calculate a percentage (%) take the number, divide by the total and multiple by 100.
• Percentages are useful in Psychology for displaying data, summarising results and are often used in data analysis to form conclusions.
• Percent means 'out of 100' and is denoted by the symbol %
• To change a fraction to a percentage, divide the numerator by the denominator and multiply by 100 (move the decimal point two places to the left).
• To change a decimal to a percentage, move the decimal point two places to the right.
• Correlations measure the relationship between two or more variables.
• Correlations calculate coefficients to show the type and strength of the relationship between the variables.
• A positive correlation has a coefficient between 0 and +1, the closer it is to +1 the stronger the correlation.
• A negative correlation has a coefficient between 0 and -1, the closer it is to -1 the stronger the correlation.
• Correlations can be weak (closer to 0) or strong (closer to 1).
• Correlations can be perfect if the coefficients are either +1 (perfect positive) or -1 (perfect negative).
• Correlations are displayed in scattergrams.
• When no correlation is seen a coefficient of zero will show.
• A positive correlation is found as one variable increases so does the other.
• A negative correlation is found as one variable increases, the other decreases.
• A perfect positive correlation is +1 and a perfect negative correlation is -1.
• No correlation means there is no relationship between the variables.