Question

Nadia's class took a math test. The median score on the test was 72% and the mean of the test scores was 72%. What does this tell you about the data set?The data is symmetrical.

The data shows causation.
The data shows a correlation.
The data is accurate.

Answer 1

The data is symmetrical

Explanation:

From the question given, it is observed that the mean value of the math test is equal to the median value of the math test.

1) A data set is symmetrical if the mean and the median are of the same value. The data set will have zero skewness

The above given data set will be symmetrical if the mean = median = 72%

Since the values are equal, we conclude that the data set is symmetrical.

2) A statistical data set shows causation when a value depends on another i.e if median depends on the mean or the mean depends on the median.

However, the mean and median values given do not depend on each other, hence, the data set does not show causation

3) A data set shows correlation when two values have a proportional relation i.e if one increases, the other decreases.

From the data set, the mean and the median do not have a proportional relation, hence they are not correlated.

4) A data set is accurate when there is a representation of the most typical value in the data set.

Since the data set does not provide us with the most typical value we cannot conclude that the data set is accurate.

Answer 2

Answer: The data is symmetrical.

Explanation:

A set of data is symmetrical when the shape of the graph is mirrored almost exactly around the middle (The graph is not skewed).

This happens when the mean (the average of the values) coincides with the median (the value in the middle of the range)

Here we have that the mean is 72% and the median is 72%, so this date set is symmetrical.