A museum surveyed three groups of 5 members to find out how many times the members visited the zoo in the past year. The table shows the results of the three samples.

Survey Visits to the Museum

Group 1 {4, 10, 6, 3, 8}

Group 2 {3, 1, 2, 1, 2}

Group 3 {7, 9, 3, 4, 7}

Identify any surveys that are likely biased. Based on the unbiased surveys, estimate the mean number of visits per member in the past year.

Round to the nearest whole number.

Sample which doesn't cover the summary of the population uniformally, and does so by biasing either highly over some sub areas of population or low attention to some areas is called biased sample. It can be biased in many terms like it covers some information which is from a special region of population, and thus, making sample only take that special values and not generalized summary of population.

When random sampling is done and sample is not biased, for large enough samples (sample size n > 30), the sample means' distribution can be modeled by normal distribution.

Finding range for this case can help as it may tell whether a large range of observations are obtained or some small range is obtained. Large range with not much outlier can tell that a good summary is observed instead of only observing specific small range.

Mean and range of group 1: {4, 10, 6, 3, 8}

Mean = (4+10+6+3+8)/5 = 6.2

Range of group = max - min = 10 - 3 = 7

Mean and range of group 2: {3, 1, 2, 1, 2}

Mean = (3+1+2+1+2)/5 = 1.8

Range of group = max - min = 3 - 1 = 2

Mean and range of group 3 {7, 9, 3, 4, 7}

Mean = (7+9+3+4+7)/5 = 5.6

Range of group = max - min = 9 - 3 = 6

Thus, the mean number of visits per member in the past year of unbiased survey is of group 1 and is 6.2

Learn more about sampling techniques here:

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