ATI TEAS GUIDE TO MATH | UNDERSTANDING DATA INTERPRETATION

UNDERSTANDING DATA INTERPRETATION

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DATA INTERPRETATION – Full Page Slides

DATA INTERPRETATION – Multiple Slides

DATA INTERPRETATION – Slides with Notes

QUIZ QUESTIONS LISTED AT END OF REVIEW

Data interpretation questions ask the applicant to interpret data given in different types of graphs. Additional questions may ask you to distinguish between dependent and independent variables in a description of an event.

The pie chart above shows visually how a whole is divided into parts. Another data interpretation graph is a line chart, which shows change over time.

Like the line chart, the bar chart also shows changes over time. However, this type of chart uses bars, rather than lines, to indicate a value.

READING GRAPHS

Data interpretation questions on the ATI TEAS are similar to some of the reading questions we reviewed in earlier videos. However, in the math portion of the ATI TEAS, questions are more likely to be complex.

DEPENDENT VERSUS INDEPENDENT VARIABLES

Dependent and independent variables are defined by the relationship between two factors.

• Dependent variable is the factor being acted upon
• Independent variable is the factor that influences the outcome

In cause-and-effect terms, we can say that the dependent variable is the effect and the independent variable is the cause.

For example: Certain plant fertilizers help plants grow more

• Independent variable: Type of fertilizer given to the plant
• Dependent Variable: Plant height

COVARIANCE

Covariance is defined as the measurement of a joint variability of two random variables.

For example: if the value of x increases when the value of y increases, then the value of x decreases when the value of y decreases. This would make x and y have positive covariances.

For example: if the value of x increases when the value of y decreases, then the value of x decreases when the value of y increases. This would make x and y have negative covariances.

MEASUREMENTS OF CENTRAL TENDENCY

Measurements of central tendency measure the mean, median, and mode of values.

• The mean of a data set is the average of the values.
  • Add up all the values and divide that sum by the total number of values
• The median is the middle number in an ordered set of values.
  • Place all the values in an increasing order. If there are an odd number of values, the median value is the middle number. If there are an even number of values, the median value is the average of the two middle values.
• The mode is the value that occurs the most in a data set. Important note: some data sets do not have a mode and some may have more than one.

For example: Find the mean, median, and mode of this data set: {4, 8, -1, 6, 4, 8, -4}

The mean is found by adding all 7 values and dividing the sum by 7. 4 + 8 + -1 + 6 + 4 + 8 + -4 = 25. The mean is 25/7 or 3.6.

The median is found by placing the values in order: -4, -1, 4, 4, 6, 8, 8. The median (middle) value is 4.

The mode is the most frequently occurring value. In this data set there are two mode values: 4 and 8.

UNDERSTANDING RANGE

The range is found by subtracting the smallest value from larger value of a data set. For the data set we previously used, {4, 8, -1, 6, 4, 8, -4}, the range is 8 – (-4) = 12.

UNDERSTANDING DATA DISTRIBUTION

The shape of a data distribution may reveal one of two distribution categories.

• A symmetrical distribution can be divided at the center and will create a mirror image on the left and right of the dividing line.
• A uniform distribution shows points spread evenly over the range of the data, but many data sets show peaks when graphed.
  • A graph with a single peak is called unimodal
  • A graph with a peak in the center and is symmetrical is called a bell-shape graph or a normal distribution
  • A graph with a single peak to the left of center (with fewer higher values on the right) is called a skewed right
  • A graph with a single peak to the right of center (with fewer higher values to the left) is called a skewed left
  • If only a small number of values are separated from the rest, these values are called outliers