Math Math Statistics and Data Analysis 4

Question 1

A dataset has values 12, 15, 15, 18, 20, 22, 50. Which measure of center best represents this data?

Accepted Answer

Median

Answer

The median is best because the outlier (50) skews the mean, making the median a more representative center.

Question 2

In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?

Accepted Answer

95%

Answer

The empirical rule states that approximately 95% of data falls within two standard deviations of the mean in a normal distribution.

Question 3

A survey finds a correlation of r = -0.85 between hours of TV watched and GPA. What does this indicate?

Accepted Answer

There is a strong negative association between the variables

Answer

r = -0.85 indicates a strong negative linear association, but correlation does not imply causation.

Question 4

Which sampling method divides the population into groups and randomly selects entire groups?

Accepted Answer

Cluster sampling

Answer

Cluster sampling divides the population into groups (clusters) and randomly selects entire clusters to survey.

Question 5

A box plot shows Q1 = 30, Q2 = 45, Q3 = 60. What is the interquartile range (IQR)?

Accepted Answer

30

Answer

IQR = Q3 − Q1 = 60 − 30 = 30.

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