This section tests your knowledge of various graphic representations of data, as well as your ability to analyze the data using statistics concepts.
Here are some concepts that are likely to appear on the test:
Data distributions are ways of organizing and presenting data to help show trends. Data distributions show all of the possible values in a data set and how often each of these values occur. Some important concepts involved in data distribution are center, spread, shape, and skewness. Let’s look at each of these a little more closely.
Center: Center can be either the mean or median value, depending on how the data is presented. The center is the value where half of the data is on one side and half is on the other side.
Shape: Shape is used to describe the way the data looks when it is graphed. Data distribution can be described as symmetrical (or bell-shaped) or as asymmetrical. If the graph of the data is symmetrical or bell-shaped, this means that the left side and right side of the center are mirror images of each other. The graph shown below is a symmetrical/bell-shaped graph.
On the other hand, the data distribution can also be asymmetrical or skewed. This means that the left and right side of the center are not mirror images of each other. The data can either be skewed left, meaning the data points trail more towards the left, or skewed right, meaning the data points trail more towards the right. The graphs below show graphs that are skewed left and skewed right. At first, this can be confusing because the “peak” of a graph that is skewed left is actually on the right side of the graph. Instead of looking at where the peak of the curve is, look at which side trails further out or has the longer “tail.”
Measures of Central Tendency and Dispersion
A measure of central tendency is a way to identify a typical value for a set of data. Ways to measure central tendency include mean, median, and mode:
Mean is another word for average. In order to find the mean for a set of numbers, you need to find the sum (or total) of all of the numbers, then divide that sum by the amount of numbers or values in the data set.
For example, to find the mean of 98, 95, and 83 you would add 98 + 95 + 83 to get 276. You would then divide 276 by 3 because there are 3 different numbers (98, 95, and 93). 276 divided by 3 equals 92, so the mean of this set of data is 92.
Median is the middle value when a set of numbers are put in order from least to greatest. If there is an even amount of numbers and two numbers are in the middle, you would find the average of those two numbers.
For example, to find the median of 34, 33, 38, 37, and 29, you would need to arrange the numbers in order from least to greatest:
29, 33, 34, 37, 38
Since 34 is in the middle, 34 is the median.
The following data set has two numbers that are in the middle:
12, 14, 15, 17, 20, 21
So, you would find the average of 15 and 17 to get a median of 16.
Mode is the number that appears most frequently in a set of numbers. For example, the mode of the following set of numbers is 18, because it appears 4 times in the set while other numbers appear one, two, or three times:
13, 10, 13, 18, 12, 12, 18, 18, 12, 18
If no number is repeated in a set, then that set of data has no mode.
A set of data can also have more than one mode if more than one number appears most frequently.
Dispersion refers to how much variation there is in a set of data is, or how spread out the data points are. A set of data can have a large distribution, such as 0, 4, 50, 102, 300; or a smaller distribution, such as 20, 21, 21, 23, 24. Dispersion can be measured in several different ways, such as range, interquartile range, variance, and standard deviation. These measures of dispersion are explained below:
Range: The range is the difference between the largest and smallest value in a data set. For example, if the values are 8, 3, 7, 10, and 9, the largest value is 10 and the smallest is 3, so the range is 10 – 3, or 7.
Interquartile range: Interquartile range, often referred to as IQR, is considered the “middle 50%” in a set of data. When the data is divided into quartiles, or four sections, the interquartile range is the data values that fall between the 25th percentile and the 75th percentile. The image below demonstrates how the interquartile range is the “middle 50%.” Q3 refers to the cutoff value for the 75th percentile and Q1 is the cutoff value for the 25th percentile. Therefore, the interquartile range is the difference between these two values: Q3 – Q1.
Variance: Variance is a measure of how spread out the values are from their mean, or average. It can be thought of as how “varied” the values are. Two different data sets can have the same mean, but look very different. The two data sets below both have a mean of 10, but the second data set has a much higher variance.
Set 1: 8, 8, 9, 10, 10, 12, 13
Set 2: 2, 2, 3, 8, 10, 20, 25
Standard Deviation: Standard deviation means how far the data values typically are from the average, or how spread out the data points are. A lower number for the standard deviation means that the values are more tightly clustered together, while a higher standard deviation means the values are more spread out.
And that’s some basic info about the Mathematics subject test.