Reading Data Displays
Learn to interpret and analyze different types of graphs and data displays commonly seen on standardized tests.
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Data displays (graphs and charts) are visual representations of data that make it easier to see patterns, compare values, and draw conclusions. Understanding how to read these displays is essential for success on the SAT and ACT.
Bar Graph
A bar graph uses rectangular bars to compare different categories. The height (or length) of each bar represents the value for that category.
- Bars can be vertical or horizontal
- Used for categorical (non-numerical) data
- Easy to compare different groups
Example Bar Graph: Favorite Sports
Number of students who chose each sport as their favorite
Histogram
A histogram is similar to a bar graph but shows the distribution of numerical data divided into intervals (bins). Bars touch each other because the data is continuous.
- Used for numerical data grouped into ranges
- Shows the shape of data distribution
- No gaps between bars
Example Histogram: Test Scores
Number of students scoring in each range
Dot Plot (Line Plot)
A dot plot shows data values as dots above a number line. Each dot represents one data point.
- Easy to see individual values
- Shows clusters, gaps, and outliers
- Good for small data sets
Example Dot Plot: Number of Siblings
Each dot represents one student
Circle Graph (Pie Chart)
A circle graph shows parts of a whole as sectors of a circle. The entire circle represents 100% of the data.
- Shows proportions and percentages
- All sectors should add up to 100%
- Good for comparing parts to the whole
Key Skills for Reading Data Displays
- Read the title - What is the graph showing?
- Check the axes - What do x and y represent? What is the scale?
- Look for patterns - Trends, clusters, gaps, outliers
- Extract specific values - Read exact numbers from the graph
- Make comparisons - Which is larger/smaller? By how much?
- Calculate statistics - Mean, median, mode, range from the data
Reading Frequency Tables
A frequency table organizes data by showing how many times each value occurs.
Example: Quiz Scores
| Score | Frequency |
|---|---|
| 6 | 2 |
| 7 | 4 |
| 8 | 7 |
| 9 | 5 |
| 10 | 2 |
From this table: Total students = 2+4+7+5+2 = 20; Mode = 8 (highest frequency)
Examples
Example 1: Reading a Bar Graph
Problem: Using the Favorite Sports bar graph above, answer: How many more students chose Soccer than Swimming?
Step 1: Find the value for Soccer: 15 students
Step 2: Find the value for Swimming: 5 students
Step 3: Calculate the difference: 15 - 5 = 10 more students
Example 2: Finding the Median from a Dot Plot
Problem: Using the Siblings dot plot above, find the median number of siblings.
Step 1: Count total data points: 3 + 5 + 4 + 2 + 1 = 15
Step 2: The median is the 8th value (middle of 15)
Step 3: Count from left: positions 1-3 are 0 siblings, positions 4-8 are 1 sibling
Answer: Median = 1 sibling
Example 3: Calculating Mean from a Histogram
Problem: Using the Test Scores histogram, estimate the mean score. (Use the midpoint of each interval.)
Step 1: Find midpoints: 64.5, 74.5, 84.5, 95
Step 2: Multiply each midpoint by its frequency:
64.5 x 4 = 258
74.5 x 8 = 596
84.5 x 12 = 1014
95 x 6 = 570
Step 3: Sum = 2438, Total students = 30
Step 4: Mean = 2438 / 30 = 81.27
Example 4: Using a Frequency Table
Problem: Using the Quiz Scores frequency table, find the mean score.
Step 1: Calculate sum of all scores:
(6 x 2) + (7 x 4) + (8 x 7) + (9 x 5) + (10 x 2)
= 12 + 28 + 56 + 45 + 20 = 161
Step 2: Total frequency = 20
Step 3: Mean = 161 / 20 = 8.05
Example 5: SAT-Style Data Interpretation
Problem: A survey showed that 25% of students preferred pizza, 30% preferred tacos, 20% preferred burgers, and the rest preferred salad. If 200 students were surveyed, how many preferred salad?
Step 1: Find percent for salad: 100% - 25% - 30% - 20% = 25%
Step 2: Calculate: 25% of 200 = 0.25 x 200 = 50 students
Practice
Use the data displays and tables to answer these questions.
Data for Problems 1-4: Hours of Homework per Week
| Hours | Number of Students |
|---|---|
| 0-2 | 5 |
| 3-5 | 12 |
| 6-8 | 18 |
| 9-11 | 10 |
| 12-14 | 5 |
1. How many students were surveyed in total?
2. What percentage of students do 6-8 hours of homework per week?
3. How many students do more than 8 hours of homework per week?
4. Using midpoints (1, 4, 7, 10, 13), estimate the mean hours of homework.
5. A dot plot shows the following data for number of pets:
0: 4 dots, 1: 7 dots, 2: 5 dots, 3: 3 dots, 4: 1 dot
What is the mode?
6. From the dot plot in problem 5, what is the median number of pets?
7. A circle graph shows that 40% of a budget goes to rent. If the total budget is $2,500, how much goes to rent?
8. In a bar graph, the tallest bar has a height of 45 and the shortest has a height of 12. What is the range between these values?
9. A histogram has the following frequencies for intervals: 3, 8, 15, 10, 4. How many data points are there in total?
10. If a pie chart shows 4 equal sections, what percentage does each section represent?
Click to reveal answers
- Total = 5 + 12 + 18 + 10 + 5 = 50 students
- 18/50 = 0.36 = 36%
- 9-11 hours + 12-14 hours = 10 + 5 = 15 students
- (1x5 + 4x12 + 7x18 + 10x10 + 13x5) / 50 = (5+48+126+100+65)/50 = 344/50 = 6.88 hours
- Mode = 1 (appears 7 times, most frequent)
- Total = 20, median is average of 10th and 11th values. Counting: 4 zeros, then 7 ones. 10th and 11th are both 1. Median = 1
- 40% of $2,500 = 0.40 x 2500 = $1,000
- Range = 45 - 12 = 33
- Total = 3 + 8 + 15 + 10 + 4 = 40
- 100% / 4 = 25% each
Check Your Understanding
Question 1: What is the difference between a bar graph and a histogram?
Show answer
A bar graph is used for categorical data with gaps between bars. A histogram is used for numerical data grouped into intervals with no gaps between bars. Histograms show the distribution of continuous data.
Question 2: How do you find the mode from a dot plot?
Show answer
Count the dots above each value on the number line. The value with the most dots above it is the mode. If multiple values have the same highest count, the data is multimodal.
Question 3: Why might the mean calculated from a histogram be an estimate rather than exact?
Show answer
Because histograms group data into intervals (ranges), we don't know the exact values within each interval. We use the midpoint of each interval as an estimate, which gives an approximate mean rather than the exact mean.
Question 4: What should all the percentages in a circle graph add up to?
Show answer
All percentages in a circle graph must add up to 100% because the entire circle represents the whole data set or total amount.
Next Steps
- Practice reading different types of graphs in newspapers and online
- Create your own data displays from collected data
- Continue to Grade 7 for more advanced probability and statistics