# Free IMSA Statistical Analysis Questions and Answers

#### What is the mode of the following set of numbers: 2, 4, 4, 4, 6, 7, 8, 9?

The mode is the number that appears most frequently in the data set, which is 4 in this case.

#### Which of the following is a measure of variability?

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

#### What type of correlation exists if an increase in one variable corresponds to an increase in another variable?

A positive correlation means that as one variable increases, the other variable also increases.

#### In a normal distribution, what percentage of data falls within one standard deviation of the mean?

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

#### What is the median of the following set of numbers: 7, 3, 9, 12, 15?

The median is the middle number when the data set is ordered: 3, 7, 9, 12, 15. The middle number is 9.

#### What does a p-value less than 0.05 indicate in a hypothesis test?

A p-value less than 0.05 indicates that there is strong evidence against the null hypothesis, so it is rejected.

#### Which of the following measures of central tendency is most affected by outliers?

The mean is most affected by outliers because it takes into account all values, while the median and mode are less affected.

#### What is the interquartile range (IQR) of the following dataset: 1, 3, 7, 9, 12, 15, 18, 20?

IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Here, Q1 is 6 and Q3 is 14. So, IQR = 14 - 6 = 8.

#### What is the mean of the following set of numbers: 4, 8, 15, 16, 23, 42?

The mean is calculated by adding all the numbers and dividing by the count: (4 + 8 + 15 + 16 + 23 + 42) / 6 = 19.

#### If a dataset has a mean of 50 and a standard deviation of 5, what is the z-score of a data point that is 60?

The z-score is calculated as (X - mean) / standard deviation. (60 - 50) / 5 = 2.

#### Which graphical representation is best used to show the distribution of a data set?

A histogram is used to show the distribution of a data set by grouping data points into ranges.