Question Type 3: Finding the quartiles using the cumulative frequency graph Exercises

A cumulative frequency graph for 40 adults’ weights (kg) is drawn through the points below.

Data (points on the cumulative frequency curve):

Estimate $Q_1$, $Q_3$, and the IQR. Give answers to 1 decimal place if needed.

The cumulative frequency graph for metal rod lengths (cm) passes through the points below.

Estimate $Q_1$, the median, $Q_3$, and the IQR. Give answers to 1 decimal place where necessary.

Heights (cm) of 48 seedlings are displayed with a cumulative frequency graph through the points below.

Data (points on the cumulative frequency graph):

Estimate $Q_1$, median, $Q_3$, and the IQR. Give answers to 1 decimal place where necessary.

Estimate the interquartile range (IQR). Give your answer to 1 decimal place.

The cumulative frequency graph of test scores (out of 60) is drawn by plotting the points below and joining them with straight segments.

Data (points on the cumulative frequency curve):

Estimate $Q_1$, the median, $Q_3$, and the interquartile range (IQR). Give answers to 1 decimal place where necessary.

A cumulative frequency graph for 50 task completion times (minutes) includes a zero-frequency class. The graph connects the points below with straight line segments.

Data (points on the cumulative frequency graph):

Estimate the median and the interquartile range (IQR). Give your answers to 1 decimal place where necessary.

The cumulative frequency graph for ages (years) of $64$ museum visitors passes through the points below.

Data (points on the cumulative frequency curve):

Estimate the median and IQR. Give answers to 1 decimal place where necessary.

Reaction times (ms) for 200 participants are summarized by the cumulative frequency curve through the points below.

Data (points on the cumulative frequency curve):

Estimate the median and the IQR. Give answers to 1 decimal place where necessary.

Estimate the median and IQR. Give answers to 1 decimal place.

The cumulative frequency graph for car speeds (km/h) is based on unequal class widths and passes through the points below.

Data (points on the cumulative frequency curve):

Estimate $Q_1$, the median, $Q_3$, and the IQR. Give answers to 1 decimal place where necessary.

The cumulative frequency graph for 80 athletes’ sprint times (in seconds) is drawn through the points below.

Estimate the median and the interquartile range (IQR). Give answers to 1 decimal place where necessary.

Two classes sat the same test. Their cumulative frequency graphs are summarised by the points below.

Class A data (points on the cumulative frequency curve):

Class B data (points on the cumulative frequency curve):

For each class, estimate the IQR, then state which class has the larger IQR. Give answers to 1 decimal place where necessary.