Question

descriptive statistics approximating the mean of a date set given a histogram some researchers developing a new intelligence test are trying to decide the maximum time to allow for completion of the test. the researchers have recorded the time for completion of the test for each of 28 participants who took the test for practice. the histogram below summarizes the completion time information for these 28 participants. based on the histogram, estimate the mean time for completion (in seconds) for the participants 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 - point of each class

The class intervals (assuming equal width, since it's a histogram for this type of problem) and their mid - points:

• For the interval \(500 - 700\), mid - point \(x_1=\frac{500 + 700}{2}=600\)
• For the interval \(700 - 900\), mid - point \(x_2=\frac{700+900}{2}=800\)
• For the interval \(900 - 1100\), mid - point \(x_3=\frac{900 + 1100}{2}=1000\)
• For the interval \(1100 - 1300\), mid - point \(x_4=\frac{1100+1300}{2}=1200\)
• For the interval \(1300 - 1500\), mid - point \(x_5=\frac{1300 + 1500}{2}=1400\)

Step2: Use the formula for the mean of a grouped data \(\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{\sum_{i=1}^{n}f_i}\)

Here, \(f_1 = 7\), \(f_2=9\), \(f_3 = 6\), \(f_4=5\), \(f_5 = 1\)
\(\sum_{i=1}^{n}f_ix_i=f_1x_1 + f_2x_2+f_3x_3+f_4x_4+f_5x_5\)

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\(\sum_{i = 1}^{n}f_i=7 + 9+6+5+1=28\)

Step3: Calculate the mean

\(\bar{x}=\frac{24800}{28}\approx885.7\)

Answer:

\(885.7\)