Question

question
estimate the mean of the number of spider webs found in randomly selected backyards given in the following grouped frequency table.

• round the final answer to two decimal places.

value interval	frequency
4 - 7	10
8 - 11	9

provide your answer below:
mean estimate = \boxed{} spider webs

Explanation:

Step1: Find midpoints of intervals

For \(0 - 3\), midpoint \(x_1=\frac{0 + 3}{2}=1.5\)
For \(4 - 7\), midpoint \(x_2=\frac{4 + 7}{2}=5.5\)
For \(8 - 11\), midpoint \(x_3=\frac{8 + 11}{2}=9.5\)

Step2: Calculate \(f_i\times x_i\) for each interval

\(f_1 = 11\), so \(f_1x_1=11\times1.5 = 16.5\)
\(f_2 = 10\), so \(f_2x_2=10\times5.5 = 55\)
\(f_3 = 9\), so \(f_3x_3=9\times9.5 = 85.5\)

Step3: Find total frequency \(N\)

\(N=f_1 + f_2 + f_3=11 + 10 + 9 = 30\)

Step4: Find total of \(f_i\times x_i\)

\(\sum f_ix_i=16.5 + 55 + 85.5 = 157\)

Step5: Calculate mean \(\bar{x}=\frac{\sum f_ix_i}{N}\)

\(\bar{x}=\frac{157}{30}\approx5.23\)

Answer:

\(5.23\)