Presentation & Display of Quantitative Data (College Board AP® Psychology): Revision Note

Tables

• Researchers use tables to present a clear summary of their findings

• Raw scores are not displayed in tables

  • Instead, data is converted into descriptive statistics to provide an overview of the results per condition

• The mean and standard deviation are the most commonly used measures in research tables:

  • The mean represents the average score per condition

  • The standard deviation indicates how spread out scores are around the mean in each condition

How to interpret a table

• Always interpret both the mean and the standard deviation

  • Do not simply describe the numbers, but explain what they tell us about participants' performance

• Example:

  • The mean score for recall of faces (10.75) is higher than the mean score for recall of names (8.32)

    • This suggests that participants recalled more faces than names on average, indicating that faces may be more distinctive and memorable than names

  • The standard deviation is higher in the faces condition (3.64) than in the names condition (1.08)

    • This suggests that performance was more variable in the faces condition, possibly due to individual differences in face recognition ability

    • In the names condition, scores clustered more closely around the mean, indicating more consistent performance across participants

Bar charts

• A bar chart is used to display discrete, categorical data

  • This is data that falls into separate, distinct categories rather than along a continuous scale

• Bar charts are used to compare scores or frequencies across different conditions or groups, e.g.:

  • Mean anxiety scores across three treatment conditions

  • Number of participants selecting each response option on a survey

• Key features of a bar chart:

  • The x-axis displays the categories or conditions being compared

  • The y-axis displays the score, frequency, or percentage for each category

  • There are gaps between the bars

    • This distinguishes bar charts from histograms and reflects the discrete, categorical nature of the data

How to interpret a bar chart

• Identify which condition or category has the highest and lowest bar

  • This tells you which group scored highest or lowest on the measure

• Compare the height of the bars across conditions to identify trends and differences

• Example:

  • If a bar chart shows mean stress scores of 24 for a control group and 12 for a mindfulness group, this suggests that participants in the mindfulness group reported considerably lower stress on average than those in the control group

• Always link your interpretation back to the research topic

  • Do not simply describe the bar heights, but explain what the difference means in the context of the study

Histograms

• A histogram is used to display continuous data

  • This is data that falls along an unbroken scale where any value within a range is possible

• Histograms show the frequency with which scores fall within each interval on the scale, e.g.:

  • The frequency of participants scoring within each 10-point range on a depression scale

  • The frequency of participants sleeping within each one-hour interval on a sleep duration measure

• Key features of a histogram:

  • The x-axis displays the continuous scale being measured, divided into equal intervals

  • The y-axis displays the frequency of scores falling within each interval

  • There are no gaps between the bars

    • This reflects the continuous nature of the data

    • A gap only appears when a particular interval has zero frequency

• The shape of a histogram reveals the distribution of scores in the data set:

  • A symmetrical, bell-shaped histogram indicates a normal distribution

  • A histogram skewed to the left or right indicates a skewed distribution

How to interpret a histogram

• Identify where scores cluster

  • Is the distribution symmetrical or skewed?

• Identify the interval with the highest frequency

  • This is where most scores fall

Example:

• If a histogram of exam scores shows the highest frequency bar in the 70–80 range with bars decreasing symmetrically on either side, this suggests that most participants scored around 70–80, with fewer participants scoring at the extremes

  • This is consistent with a normal distribution

Scatterplots

• A scatterplot is used to display the results of correlational research

  • It shows the relationship between two co-variables

• Each point on the scatterplot represents one participant's scores on both co-variables

  • One score is plotted on the x-axis and the other on the y-axis

• The pattern of points on the scatterplot indicates the direction and strength of the relationship between the co-variables:

  • Positive correlation — points trend upward from left to right

    • As one co-variable increases, the other also increases

  • Negative correlation — points trend downward from left to right

    • As one co-variable increases, the other decreases

  • Zero correlation — points are scattered with no clear pattern

    • There is no relationship between the co-variables

• Either co-variable can be placed on either axis

  • The direction of the correlation will be the same regardless of which axis is chosen

How to interpret a scatterplot

• Identify the direction of the relationship

  • Is the trend positive, negative, or absent?

• Assess the strength of the relationship

  • Are the points tightly clustered around an imaginary line (strong correlation) or widely scattered (weak correlation)?

• Identify any outliers

  • Individual points that fall far from the general trend may be distorting the overall pattern

• Always link interpretation to the correlation coefficient

  • The scatterplot shows the direction and approximate strength visually, but the correlation coefficient provides the precise numerical value

• Example

  • A scatterplot showing a clear upward trend with tightly clustered points, accompanied by a correlation coefficient of +0.85, indicates a strong positive relationship between the two co-variables