Statistical RepresentationsEdexcel GCSE Maths: Flashcards
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What is a bar chart used to represent?
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- What is a bar chart used to represent?
- A bar chart is used to represent categorical data or discrete data. The height of each bar represents the frequency of each category. Bars are separated by equal spaces and all have the same width.
- How do you construct a pie chart?
- To construct a pie chart: calculate the angle for each category using (frequency ÷ total frequency) × 360°. Draw a circle and use a protractor to mark off each angle. Label each sector with its category and frequency or percentage.
- Define frequency density.
- Frequency density is the frequency divided by the class width. It is calculated using the formula: frequency density = frequency ÷ class width. It is used in histograms with unequal class widths.
- How do you construct a histogram with unequal class widths?
- Calculate frequency density for each class using: frequency density = frequency ÷ class width. The height of each bar represents the frequency density (not frequency). The area of each bar represents the frequency.
- What is a cumulative frequency graph?
- A cumulative frequency graph shows the running total of frequencies plotted against the upper class boundary of each class. Points are joined with a smooth curve. It is used to find the median, quartiles and interquartile range.
- How do you find the median from a cumulative frequency graph?
- Find the median by locating the value of total frequency ÷ 2 on the cumulative frequency axis. Draw a horizontal line to meet the curve, then draw a vertical line down to read the value on the horizontal axis.
- Define a box plot and name its five key values.
- A box plot is a diagram that displays the distribution of data. Its five key values are: minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value. The box shows the interquartile range and a line inside shows the median.
- What is the interquartile range (IQR)?
- The interquartile range is the difference between the upper quartile and the lower quartile: IQR = Q3 − Q1. It represents the range of the middle 50% of the data and is a measure of spread that is not affected by outliers.
- How do you compare distributions using box plots?
- Compare box plots by examining: the medians (central tendency), the interquartile ranges (spread of the middle 50%), the ranges (overall spread), and the positions of the quartiles. Comment on which distribution is higher, more spread out, or more skewed.
- What does a scatter diagram show?
- A scatter diagram plots two variables as points on a graph with one variable on each axis. It shows the relationship (correlation) between the two variables and whether they are related.
- Define positive, negative and zero correlation.
- Positive correlation: as one variable increases, the other increases. Negative correlation: as one variable increases, the other decreases. Zero correlation: there is no linear relationship between the variables.
- What is a line of best fit on a scatter diagram?
- A line of best fit is a straight line drawn through scatter diagram data to show the general trend. It should have approximately equal numbers of points above and below the line. It can be used to estimate values within the range of data.
- What is a time series graph used for?
- A time series graph plots data points against time on the horizontal axis. It shows how a variable changes over time and reveals trends, patterns, and seasonal variations in the data.
- How do you interpret trends in a time series graph?
- Look at the direction of the line or points: an upward trend indicates the variable is increasing over time; a downward trend indicates it is decreasing. A horizontal trend indicates no change. Identify any seasonal patterns that repeat at regular intervals.
- What is a pictogram and how is it constructed?
- A pictogram is a diagram that uses symbols or pictures to represent frequencies. Each symbol represents a certain frequency (which is stated in the key). Parts of symbols can be used to represent fractional frequencies, such as half or quarter symbols.
- What is a stem-and-leaf diagram?
- A stem-and-leaf diagram displays data by splitting each number into a stem (the first digit(s)) and a leaf (the last digit). The stem is written in the centre and leaves are written to the right (or both sides for back-to-back diagrams). Data is shown in order and the diagram shows the distribution.