Question

home realty claims that the mean selling time of a detached, residential house is 30 or fewer days after it is listed with the company. not ready to believe home, you sample 17 customers who sold a detached, residential house through home and record the selling times (in days) of the houses. your data are summarized in the following histogram. based on the histogram, estimate the mean selling time (in days) for the sample of houses. carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

Explanation:

Step1: Find the mid - points of each class interval

Assume the class intervals are \(0 - 10\), \(10 - 20\), \(20 - 30\), \(30 - 40\), \(40 - 50\). The mid - points \(x_i\) are calculated as \(\frac{0 + 10}{2}=5\), \(\frac{10+20}{2} = 15\), \(\frac{20 + 30}{2}=25\), \(\frac{30+40}{2}=35\), \(\frac{40 + 50}{2}=45\)

Step2: Find the product of mid - points and frequencies

The frequencies \(f_i\) are \(3\), \(5\), \(5\), \(2\), \(2\) respectively.
The products \(f_ix_i\) are:
For \(i = 1\): \(f_1x_1=3\times5 = 15\)
For \(i = 2\): \(f_2x_2=5\times15=75\)
For \(i = 3\): \(f_3x_3=5\times25 = 125\)
For \(i = 4\): \(f_4x_4=2\times35=70\)
For \(i = 5\): \(f_5x_5=2\times45 = 90\)

Step3: Calculate the sum of frequencies and the sum of \(f_ix_i\)

\(\sum f_i=3 + 5+5+2+2=17\)
\(\sum f_ix_i=15 + 75+125+70+90=375\)

Step4: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum f_ix_i}{\sum f_i}\)
\(\bar{x}=\frac{375}{17}\approx22.0588\)

Answer:

\(22.1\)