Data Displays: Histograms and Box Plots
Grade 6 · Math · Study Guide
Learn to read, create, and interpret histograms and box plots to analyze data.
A histogram looks like a bar graph, but it shows how frequently data falls within certain ranges (called intervals or bins). The bars in a histogram touch each other because the data is continuous — there are no gaps. The horizontal axis shows the data ranges, and the vertical axis shows frequency (how many values fall in each range). Histograms are great for seeing the overall shape and spread of a large data set.
A box plot (also called a box-and-whisker plot) summarizes data using five key values: the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum. The box itself spans from Q1 to Q3 — this range is called the interquartile range (IQR). The line inside the box is the median. Whiskers extend from the box to the minimum and maximum values.
The IQR = Q3 − Q1 and tells you how spread out the middle 50% of your data is. A small IQR means data is clustered together; a large IQR means it's more spread out.
Box plots make it easy to compare two data sets side by side. Histograms show you the shape of distribution — is the data symmetric, skewed left, or skewed right? These two displays answer different questions about the same data.
| Term | What It Is | Position in Box Plot |
|---|---|---|
| Minimum | Smallest value in the data set | Left whisker end |
| Q1 | 25th percentile — middle of lower half | Left side of box |
| Median (Q2) | Middle value of the data set | Line inside box |
| Q3 | 75th percentile — middle of upper half | Right side of box |
| Maximum | Largest value in the data set | Right whisker end |
Key terms
- Histogram
- A bar graph where bars touch, showing frequency of data in ranges (intervals)
- Box Plot
- A graph showing the five-number summary: minimum, Q1, median, Q3, maximum
- Quartile
- Values that divide a data set into four equal parts
- IQR (Interquartile Range)
- The range of the middle 50% of data: IQR = Q3 − Q1
Flashcards
- Histogram
- Bar graph with touching bars — shows frequency of continuous data in intervals
- Box plot (box-and-whisker)
- Displays five-number summary: min, Q1, median, Q3, max
- IQR
- Interquartile range = Q3 − Q1; spread of the middle 50% of data
- Median in box plot
- The line inside the box — middle value of the data set
- Whiskers in box plot
- Lines extending from box to the minimum and maximum values
- Skewed right histogram
- Data bunches on the left, tail stretches to the right
Practice questions
In a box plot, the line inside the box represents the:
- Median
- Mean
- IQR
- Maximum
Show answer
Answer: Median
The line inside the box of a box plot always shows the median (middle value) of the data set.
A data set has Q1 = 15 and Q3 = 27. What is the IQR?
- 12
- 42
- 21
- 6
Show answer
Answer: 12
IQR = Q3 − Q1 = 27 − 15 = 12.
In a histogram, the bars must touch each other (no gaps).
Show answer
Answer: True
Histograms show continuous data in ranges, so bars touch — there are no gaps between intervals.
The five-number summary includes the minimum, Q1, median, Q3, and ___.
Show answer
Answer: maximum
The five-number summary is: minimum, Q1, median (Q2), Q3, maximum.
Which plot is best for comparing the spread of two data sets?
- Box plot
- Line graph
- Pie chart
- Scatter plot
Show answer
Answer: Box plot
Box plots make side-by-side comparison of spread and center easy — you can see medians and IQRs at a glance.
Fun facts
- The box plot was invented by statistician John Tukey in 1970 — he also co-invented the Fast Fourier Transform used in digital audio and Wi-Fi.
- The shape of a histogram can tell a scientist whether data follows a normal (bell-curve) distribution, which is key for medical research and quality control.
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