Data Sets Overlap Quiz

What is the degree of overlap between the two data sets?

• None

• Low

• Moderate

• High

Answer explanation

The degree of overlap between the two data sets is 'None' because there are no common elements or similarities identified in the data sets, indicating a complete lack of overlap.

What is the median for this data set? 5, 8, 1, 3, 9, 6, 4

• 3

• 5

• 6

• 8

Answer explanation

To find the median, first sort the data: 1, 3, 4, 5, 6, 8, 9. The median is the middle value, which is 5 in this case, as it is the fourth number in the sorted list.

Identify the outlier in the following set of numbers: 75, 80, 0, 85, 90, 95, 100

• 75

• 80

• 0

• 100

Answer explanation

The outlier in the set is 0, as it is significantly lower than the other numbers, which range from 75 to 100. All other numbers are positive and closely grouped, making 0 the clear outlier.

What is a Random Sample?

• A smaller group being studied.

• A selection where each member has an equally likely chance of being chosen.

• The entire group being studied.

• Unfairly favors certain outcomes.

Answer explanation

A random sample ensures that every member of the population has an equal chance of being selected, which helps eliminate bias and allows for more accurate generalizations about the entire group.

What is the definition of Population in statistics?

• The entire group being studied.

• A smaller group being studied.

• The average distance between each data point and the mean.

• The statistical measure that represents the spread of the middle 50% of a data set.

Answer explanation

In statistics, 'Population' refers to the entire group being studied, which includes all members of a specified group. This distinguishes it from a sample, which is a smaller subset of the population.

What is the definition of range?

• The range is the average of all values in a dataset.

• The range is the sum of the maximum and minimum values in a dataset.

• The range is the difference between the maximum and minimum values in a dataset.

• The range is the total number of values in a dataset.

Answer explanation

The range is defined as the difference between the maximum and minimum values in a dataset. This means you subtract the smallest value from the largest value to find the range, making the correct choice the third option.

What is the purpose of calculating the Mean Absolute Deviation (MAD)?

• To find the spread of the middle 50% of a data set.

• To determine the average distance between each data point and the mean.

• To identify a smaller group being studied.

• To select a group where each member has an equally likely chance of being chosen.

Answer explanation

The Mean Absolute Deviation (MAD) measures the average distance of each data point from the mean, providing insight into the data's variability. This makes the second choice the correct answer.

Which measure of central tendency is most affected by outliers?

• Range

• Mean

• Median

• Mode

Answer explanation

The mean is most affected by outliers because it takes into account all values in a dataset. A single extreme value can significantly skew the mean, while the median and mode remain unaffected by such extremes.

What is the purpose of a box plot?

• To show the mean of data

• To display the distribution of data

• To calculate the sum of data

• To find the mode of data

Answer explanation

A box plot visually displays the distribution of data by showing the median, quartiles, and potential outliers, making it easier to understand the spread and skewness of the dataset.

Based on the survey data, which type of pet is least favored by teenagers?

• Cats are the least favored pet among teenagers.

• Dogs are the least favored pet among teenagers.

• Birds are the least favored pet among teenagers.

• The number of teenagers who like cats is decreasing.

Answer explanation

Survey data indicates that birds are the least favored pet among teenagers, as they received the lowest preference ratings compared to cats and dogs.