1015913172125dataFrequency[Graphs generated by this script: setBorder(54,40,20,5); initPicture(0,25,0,10);axes(1000,2,1,1000,2); fill="blue"; stroke="black";line([1,-0.2],[1,0.2]); text([1,0],"1","below");line([5,-0.2],[5,0.2]); text([5,0],"5","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([13,-0.2],[13,0.2]); text([13,0],"13","below");line([17,-0.2],[17,0.2]); text([17,0],"17","below");line([21,-0.2],[21,0.2]); text([21,0],"21","below");line([25,-0.2],[25,0.2]); text([25,0],"25","below");textabs([165,0],"data","above");textabs([0,115],"Frequency","right",90);rect([1,0],[5,10]);rect([5,0],[9,4]);rect([9,0],[13,3]);rect([13,0],[17,7]);rect([17,0],[21,2]);rect([21,0],[25,9]);]

Based on the histogram above, what is the class width?

Class width =

What is the sample size?

Sample size =

To solve this, we'll break down the details from the histogram.

### 1. **Class Width:**
   - **Class Width** is the difference between the lower bounds of two consecutive classes.
   - From the code, the classes are defined by the ranges:
     - [1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [21, 25]

   The class width can be calculated as:

   \[
   \text{Class Width} = \text{Lower Bound of Second Class} - \text{Lower Bound of First Class} = 5 - 1 = 4
   \]

   So, the **Class Width = 4**.

### 2. **Sample Size:**
   - The sample size is the total frequency of all classes.
   - From the code, the frequencies are:
     - [1, 5] → 10
     - [5, 9] → 4
     - [9, 13] → 3
     - [13, 17] → 7
     - [17, 21] → 2
     - [21, 25] → 9

   Summing these values:

   \[
   \text{Sample Size} = 10 + 4 + 3 + 7 + 2 + 9 = 35
   \]

   So, the **Sample Size = 35**.

### Summary:
- **Class Width = 4**
- **Sample Size = 35**

Do you want more details or have any questions?

Here are 5 related questions you could explore:
1. How would the histogram change if the class width was decreased?
2. What is the relative frequency of the largest class?
3. How do you interpret the mode from this histogram?
4. What would be the impact of adding more data points on the histogram?
5. How could we normalize this histogram?

**Tip:** Always check the class boundaries carefully when interpreting histograms!

Explore how to calculate class width and sample size from a histogram. Learn the concepts of class boundaries, frequency distributions, and their relevance in statistical analysis.

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