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
ATI TEAS Math Data Interpretation
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Question 1 of 8
1. Question
Most companies increase their customers with more advertising.
Which of the following is the dependent variable in the statement above?
Correct
In this statement, customers is the dependent variable. The number of customers is influenced by the level of advertising, which is the independent variable.
Incorrect
In this statement, customers is the dependent variable. The number of customers is influenced by the level of advertising, which is the independent variable.
Question 2 of 8
2. Question
A scientist is presenting a report on the results of a survey that shows the number of people taking different medications to treat the same illness. Which of the following graphs should the scientist use to visually emphasize the percentage of patients taking each medication?
Correct
A circle graph shows visually how a whole is divided into parts. It would be the best choice to use to visually emphasize the percentage of patients taking each medication.
Incorrect
A circle graph shows visually how a whole is divided into parts. It would be the best choice to use to visually emphasize the percentage of patients taking each medication.
Question 3 of 8
3. Question
The information provided below shows the number of products held in the inventory of a warehouse over a period of 5 months.
January 20 thousands, February 30 thousands, March 50 thousands, April 35 thousands, May 50 thousands
Which of the following is the difference between the largest and smallest monthly inventories shown in the information?
Correct
The largest monthly inventory is 50,000 products, held in March and May. The smallest monthly inventory is 20,000 products, held in January. To find the difference between these two, use subtraction: 50,000 – 20,000 = 30,000.
Incorrect
The largest monthly inventory is 50,000 products, held in March and May. The smallest monthly inventory is 20,000 products, held in January. To find the difference between these two, use subtraction: 50,000 – 20,000 = 30,000.
Question 4 of 8
4. Question
The information below shows the distribution of 257 units shipped by particular vendors to a company over a 6-month period.
70 from Hi Side, 33 from Lighttask, 29 from Acme, 18 from Severn, 42 from Ace Hill, 65 from Laurel
The units shipped by Severn represent what percentage of all units shipped by vendors during that period? (Round the solution to the nearest tenth of a percent.)
Correct
According to the information, Severn shipped 18 units during the 6-month period. This amounts to 18/257 of the total units shipped. Divide 18 by 257 to determine the percentage: 18 ÷ 257 = 0.07. Convert this decimal to a percentage by moving the decimal point to the right two places. The units shipped by Severn represent 7% of all units shipped.
Incorrect
According to the information, Severn shipped 18 units during the 6-month period. This amounts to 18/257 of the total units shipped. Divide 18 by 257 to determine the percentage: 18 ÷ 257 = 0.07. Convert this decimal to a percentage by moving the decimal point to the right two places. The units shipped by Severn represent 7% of all units shipped.
Question 5 of 8
5. Question
A law firm handled 116 cases over a period of one year. 17 for criminal, 35 for malpractice, 21 for divorce, 19 for custody, and 24 for probate.
Custody cases represent what percentage of all cases handled by the firm that year? (Round the solution to the nearest tenth of a percent.)
Correct
The firm handled 19 custody cases during the year, or 19/116 . Divide 19 by 116 to determine the percentage: 19 ÷ 116 is approximately 0.164. Convert this decimal to a percentage by moving the decimal point to the right two places. Custody cases represent 16.4% of all cases handled by the firm.
Incorrect
The firm handled 19 custody cases during the year, or 19/116 . Divide 19 by 116 to determine the percentage: 19 ÷ 116 is approximately 0.164. Convert this decimal to a percentage by moving the decimal point to the right two places. Custody cases represent 16.4% of all cases handled by the firm.
Question 6 of 8
6. Question
The information provided below shows the number of miles Paul drove each day last week.
Find the median, mode, and range. Put the values in increasing order: 5, 15, 15, 16, 17, 19, 43. There are 7 values, so the median is the middle value, 16. Mode is 15. The range is 43 – 15 = 28. Ordering those values gives you mode < median < range.
Incorrect
Find the median, mode, and range. Put the values in increasing order: 5, 15, 15, 16, 17, 19, 43. There are 7 values, so the median is the middle value, 16. Mode is 15. The range is 43 – 15 = 28. Ordering those values gives you mode < median < range.
Question 7 of 8
7. Question
Stock prices usually decrease when investors panic.
Which of the following is the independent variable in the event described above?
Correct
In this statement, the cause is panic of investors, and the effect is the decrease in stock prices. Investor panic is the independent variable, because it influences the outcome of stock price decline.
Incorrect
In this statement, the cause is panic of investors, and the effect is the decrease in stock prices. Investor panic is the independent variable, because it influences the outcome of stock price decline.
Question 8 of 8
8. Question
Which of the following describes negative covariance?
Correct
Negative covariance occurs when one variable increases as the other decreases. This is the case in choice A. As time increases, stress decreases.
Incorrect
Negative covariance occurs when one variable increases as the other decreases. This is the case in choice A. As time increases, stress decreases.
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