The graph below shows cumulative proportions plotted against...

The graph below shows cumulative proportions plotted against grade point averages for a large public high school. What are the median grade point average and the IQR? (A) Median $=0.8, \mathrm{IQR}=1.8$ (B) Median $=2.0, \mathrm{IQR}=2.8$ (C) Median $=2.4, \mathrm{IQR}=1.0$ (D) Median $=2.5, \mathrm{IQR}=1.0$ (E) Median $=2.6, \mathrm{IQR}=1.8$

The graph below shows cumulative proportions plotted against grade point averages for a large public high school. What are the median grade point average and the IQR?
(A) Median $=0.8, \mathrm{IQR}=1.8$
(B) Median $=2.0, \mathrm{IQR}=2.8$
(C) Median $=2.4, \mathrm{IQR}=1.0$
(D) Median $=2.5, \mathrm{IQR}=1.0$
(E) Median $=2.6, \mathrm{IQR}=1.8$

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Key Concepts

Median

The median is a measure of central tendency that represents the middle value of a dataset when arranged in order. In the context of a cumulative frequency graph, the median is the data value at which the cumulative proportion reaches 50%, indicating that half of the observations lie below this value and half lie above it.

Interquartile Range (IQR)

The interquartile range (IQR) is a measure of variability that represents the range between the first quartile (25th percentile) and the third quartile (75th percentile). The IQR provides a measure of the spread of the middle 50% of the data, and it is especially useful for understanding the distribution in a cumulative frequency graph without being influenced by extreme values.

Cumulative Frequency Graph

A cumulative frequency graph plots the cumulative proportion or frequency of data points below a specific value, allowing one to see the distribution of the dataset. As one moves along the horizontal axis, the graph shows the proportion of observations that fall at or below that value, making it an effective tool to identify percentiles and quartiles in a dataset.

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