Histograms Worksheets - 15 Worksheets Library - Free Printable

Let's solve the problem step by step.

---

Step 1: Understand the Data

We are given a list of numbers representing the number of books:

Data:
4, 1, 13, 16, 28, 25, 31, 33, 34, 32, 49, 41, 43, 49, 49

There are 15 data points.

---

Step 2: Create Frequency Distribution Table

We need to group the data into intervals and count how many values fall into each interval.

The intervals are:

- 0–10
- 11–20
- 21–30
- 31–40
- 41–50

Let’s go through each number and assign it to the correct group.

#### Tallying the Data

| Number | Group |
|--------|-------------|
| 4 | 0–10 |
| 1 | 0–10 |
| 13 | 11–20 |
| 16 | 11–20 |
| 28 | 21–30 |
| 25 | 21–30 |
| 31 | 31–40 |
| 33 | 31–40 |
| 34 | 31–40 |
| 32 | 31–40 |
| 49 | 41–50 |
| 41 | 41–50 |
| 43 | 41–50 |
| 49 | 41–50 |
| 49 | 41–50 |

Now, count the frequency for each group:

- 0–10: 4, 1 → 2
- 11–20: 13, 16 → 2
- 21–30: 28, 25 → 2
- 31–40: 31, 33, 34, 32 → 4
- 41–50: 49, 41, 43, 49, 49 → 5

---

Step 3: Fill in the Frequency Distribution Table

| Number of books | Tally | Frequency |
|------------------|-------|-----------|
| 0–10 | || | 2 |
| 11–20 | || | 2 |
| 21–30 | || | 2 |
| 31–40 | |||| | 4 |
| 41–50 | |||| | | 5 |

> Note: Tally marks are usually written as vertical lines (|), with a diagonal line across every fifth one. So:
> - 2 = ||
> - 4 = ||||
> - 5 = |||| |

---

Step 4: Draw the Histogram

Now we draw the histogram based on the frequency distribution.

- The x-axis represents the groups: 0–10, 11–20, 21–30, 31–40, 41–50.
- The y-axis represents frequency (from 0 to 6, since max frequency is 5).

We draw bars for each group with height equal to the frequency.

#### Bar Heights:
- 0–10 → height = 2
- 11–20 → height = 2
- 21–30 → height = 2
- 31–40 → height = 4
- 41–50 → height = 5

---

Final Answer

#### ✔ Completed Table:

| Number of books | Tally | Frequency |
|------------------|-------|-----------|
| 0–10 | || | 2 |
| 11–20 | || | 2 |
| 21–30 | || | 2 |
| 31–40 | |||| | 4 |
| 41–50 | |||| | | 5 |

---

#### ✔ Histogram Description (to draw):

On the provided grid:

- Label x-axis: Groups (0–10, 11–20, 21–30, 31–40, 41–50)
- Label y-axis: Frequency (0 to 6)
- Draw bars:
- 0–10: height 2
- 11–20: height 2
- 21–30: height 2
- 31–40: height 4
- 41–50: height 5

Each bar should be of equal width and touch the next (since it's a histogram).

---

✔ Summary

- We grouped the data into classes.
- Counted frequencies.
- Created a tally and frequency table.
- Prepared the histogram accordingly.

This completes the task!

Let me know if you'd like a visual representation drawn here!