The class 12 < t ≤ 24 has cumulative total 17. Sam plots (18, 17). Why does the table not support that point?

• The midpoint 18 belongs on the frequency axis instead of the time axis.
• Using a midpoint always makes cumulative totals decrease as values increase.
• The upper boundary 24 must replace the frequency total of 17.
• The total belongs at 24; the count at 18 is unknown.

A cumulative frequency curve counts values at or below each horizontal-axis value. What does its height at 35 tell you?

• how many values are exactly 35
• how many values are 35 or less
• how many values are more than 35
• how many classes end at 35

The last point on a cumulative frequency curve is at a height of 124. What does that say?

• The largest value in the data is 124
• There are 124 classes
• There are 124 values altogether
• The largest class holds 124 values

An at-or-below cumulative relative frequency graph for 150 values reads 0.4 at 18. Estimate the number of values at or below 18.

A curve of 160 values gives a lower quartile of 22 and an upper quartile of 39. What is the interquartile range?

An at-or-below curve for 60 runners reads 48 at 35 minutes. Leo reports 48 runners taking longer than 35 minutes. What should he report?

• About 12: subtract the 48 already finished from all 60.
• About 48: the reading counts those still running after 35.
• About 24: halve the reading because 35 splits the times.
• About 60: the final height counts everyone finishing late.

A median estimated from grouped data using a cumulative frequency curve must equal the exact median of the raw values.

An at-or-below cumulative frequency graph reads 18 at 12 and 45 at 28. Estimate how many values satisfy 12 < x ≤ 28.

A grouped table's first nonempty class is 15 ≤ w < 20. What can you conclude about the actual minimum?

• It equals 15 because the first class starts at that boundary.
• It equals 20 because plotting uses upper class boundaries.
• It is at least 15 but less than 20.
• It equals 17.5 because every class uses its midpoint as an observation.

Cumulative curves A and B have totals 64 and 192. Coordinates are (value, cumulative frequency). A has points (31, 16), (43, 32), (52, 48); B has (35, 48), (43, 96), (58, 144). Which comparison of group sizes and median estimates is supported?

• A has three times as many values; both median estimates are 43.
• B has three times as many values; both median estimates are 43.
• B has three times as many values; the median estimates are 31 for A and 35 for B.
• B has three times as many values; the median estimates are 52 for A and 58 for B.