A botany student measured the lengths of a sample of leaves to the nearest centimeter. The data is shown in the frequency distribution below. Use the data to approximate the mean to the nearest Tenth of a centimeter.

$\begin{array} { | c | c | }
\hline \text { Length } & \text { Frequency } \
\hline 0 - 5 & 4 \
\hline 6 - 11 & 7 \
\hline 12 - 17 & 13 \
\hline 18 - 23 & 18 \
\hline 24 - 29 & 8 \
\hline 30 - 35 & 5 \
\hline
\end{array}$

A) 18.2 cm
B) 9.2 cm
C) 18.7 cm
D) 5.8 cm

Question

A botany student measured the lengths of a sample of leaves to the nearest centimeter. The data is shown in the frequency distribution below. Use the data to approximate the mean to the nearest Tenth of a centimeter.

$\begin{array} { | c | c | } 
\hline \text { Length } & \text { Frequency } \
\hline 0 - 5 & 4 \
\hline 6 - 11 & 7 \
\hline 12 - 17 & 13 \
\hline 18 - 23 & 18 \
\hline 24 - 29 & 8 \
\hline 30 - 35 & 5 \
\hline
\end{array}$

A) 18.2 cm
B) 9.2 cm
C) 18.7 cm
D) 5.8 cm

Quizplus · Accepted Answer

We can approximate the mean by finding the midpoint of each interval and computing the weighted average of the data.

Midpoints:
2.5, 8.5, 14.5, 20.5, 26.5, 32.5

Weighted average:
((2.5*4)+(8.5*7)+(14.5*13)+(20.5*18)+(26.5*8)+(32.5*5))/55 ≈ 18.7

Therefore, the best choice is C.

A Botany Student Measured the Lengths of a Sample of Leaves