In a survey carried out at the University of California,...

In a survey carried out at the University of California, Berkeley, a sample of students were interviewed and asked what their grade-point average was. A histogram of the results is shown below. (GPA ranges from 0 to $4,$ and 2 is a bare pass.) $\begin{array}{l}{\text { (a) True or false: more students reported a GPA in the range } 2.0 \text { to } 2.1 \text { than }} \\ {\text { in the range } 1.5 \text { to } 1.6 .} \\ {\text { (b) True or false: more students reported a GPA in the range } 2.0 \text { to } 2.1 \text { than }} \\ {\text { in the range } 2.5 \text { to } 2.6 \text { . }} \\ {\text { (c) What accounts for the spike at 2? }}\end{array}$

In a survey carried out at the University of California, Berkeley, a sample of
students were interviewed and asked what their grade-point average was. A
histogram of the results is shown below. (GPA ranges from 0 to $4,$ and 2 is a
bare pass.)
$\begin{array}{l}{\text { (a) True or false: more students reported a GPA in the range } 2.0 \text { to } 2.1 \text { than }} \\ {\text { in the range } 1.5 \text { to } 1.6 .} \\ {\text { (b) True or false: more students reported a GPA in the range } 2.0 \text { to } 2.1 \text { than }} \\ {\text { in the range } 2.5 \text { to } 2.6 \text { . }} \\ {\text { (c) What accounts for the spike at 2? }}\end{array}$

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Key Concepts

Data Heaping (Rounding Bias)

Data heaping, also known as rounding bias, occurs when survey respondents tend to report rounded or ‘preferred’ values rather than precise measurements. This phenomenon can create spikes in a frequency distribution, where certain values are overrepresented. Recognizing such spikes is important when analyzing self-reported data, as it affects the interpretation of the underlying distribution.

Histogram Interpretation

A histogram is a graphical representation of the frequency distribution of a dataset. It groups data points into continuous intervals (also called bins) and shows how many data points fall into each interval. This visual tool is useful for identifying patterns, such as the central tendency, spread, and the shape of the distribution, as well as any outliers in the data.

Comparing Frequency Counts

Interpreting histograms often involves comparing the heights of the bars, which represent the number of observations in each interval. This allows us to determine relative frequencies among different ranges in the data, which is essential for answering questions involving comparisons between specific intervals or bins.

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