Question
What are the classes in a
Histogram
Histogram
Answers
GPT-5 mini
In a histogram, a "class" (also called a bin or interval) is one of the contiguous groupings of the data values into which you sort observations to form the frequency distribution plotted by the histogram.
Key components and terms
- Class limits: the lower and upper values that define a class (e.g., 10–19).
- Class boundaries: the true cut points between classes; these avoid gaps when values are continuous (e.g., 9.5–19.5 for integer data 10–19).
- Class width (or bin width): upper limit minus lower limit (typically constant for all classes).
- Class mark (midpoint): (lower limit + upper limit) / 2, often used to represent the class on the x-axis.
- Frequency (or relative frequency): count (or proportion) of observations in that class.
Requirements for classes
- Mutually exclusive (no overlap).
- Exhaustive (cover the entire data range).
- Usually equal width (for easy comparison), though variable-width bins are possible.
- Nonzero width (no empty/zero-size classes).
How many classes / what width to use
- Rule-of-thumb choices:
- Sturges: k = 1 + log2(n) (≈ 1 + 3.322·log10 n)
- Rice: k = 2 · n^(1/3)
- Freedman–Diaconis (bin width): h = 2·IQR / n^(1/3)
- Scott (bin width): h = 3.49·σ / n^(1/3)
- Practical tips: choose a k between about 5 and 20 depending on sample size; use "nice" round numbers for class limits; avoid too many empty or too few over-smoothed bins.
Short example
Data range = 12 to 98, choose 9 classes → class width ≈ (98 − 12)/9 ≈ 9.56 → round to 10. Classes: 10–19, 20–29, …, 90–99 (use boundaries 9.5–19.5, etc., if needed).
If you want, tell me the data or sample size and I can propose suitable classes (bins) and boundaries.
Key components and terms
- Class limits: the lower and upper values that define a class (e.g., 10–19).
- Class boundaries: the true cut points between classes; these avoid gaps when values are continuous (e.g., 9.5–19.5 for integer data 10–19).
- Class width (or bin width): upper limit minus lower limit (typically constant for all classes).
- Class mark (midpoint): (lower limit + upper limit) / 2, often used to represent the class on the x-axis.
- Frequency (or relative frequency): count (or proportion) of observations in that class.
Requirements for classes
- Mutually exclusive (no overlap).
- Exhaustive (cover the entire data range).
- Usually equal width (for easy comparison), though variable-width bins are possible.
- Nonzero width (no empty/zero-size classes).
How many classes / what width to use
- Rule-of-thumb choices:
- Sturges: k = 1 + log2(n) (≈ 1 + 3.322·log10 n)
- Rice: k = 2 · n^(1/3)
- Freedman–Diaconis (bin width): h = 2·IQR / n^(1/3)
- Scott (bin width): h = 3.49·σ / n^(1/3)
- Practical tips: choose a k between about 5 and 20 depending on sample size; use "nice" round numbers for class limits; avoid too many empty or too few over-smoothed bins.
Short example
Data range = 12 to 98, choose 9 classes → class width ≈ (98 − 12)/9 ≈ 9.56 → round to 10. Classes: 10–19, 20–29, …, 90–99 (use boundaries 9.5–19.5, etc., if needed).
If you want, tell me the data or sample size and I can propose suitable classes (bins) and boundaries.