Data, Frequency Tables, and Histograms, Oh My! - ArgoPrep - Free Printable

Let's solve the problem step by step.

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Step 1: Understand the Data

We are given a list of average temperatures in different states:

```
50, 42, 100, 45, 68, 32, 100,
67, 61, 31, 75, 39, 62, 64,
49, 55, 51, 33, 99, 96, 64
```

There are 21 temperature values.

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Step 2: Create a Frequency Table

We need to count how many temperatures fall into each interval (range):

| Temperatures | Frequency |
|--------------|-----------|
| 31 - 40 | |
| 41 - 50 | |
| 51 - 60 | |
| 61 - 70 | |
| 71 - 80 | |
| 81 - 90 | |
| 91 - 100 | |

Now go through each temperature and count how many fall in each range.

---

#### Let's sort the data first for easier counting:
Sorted temperatures:
```
31, 32, 33, 39, 42, 45, 49, 50, 51, 55, 61, 62, 64, 64, 67, 68, 75, 96, 99, 100, 100
```

Wait — let’s double-check the original list to ensure we have all 21 numbers:

Original:
- Row 1: 50, 42, 100, 45, 68, 32, 100 → 7 numbers
- Row 2: 67, 61, 31, 75, 39, 62, 64 → 7 numbers
- Row 3: 49, 55, 51, 33, 99, 96, 64 → 7 numbers

Total = 21 numbers. Let's list them all clearly:

List of temperatures:
31, 32, 33, 39, 42, 45, 49, 50, 51, 55, 61, 62, 64, 64, 67, 68, 75, 96, 99, 100, 100

Wait — that's only 21? Let's count again:

From above:
- 31 ✔
- 32 ✔
- 33 ✔
- 39 ✔
- 42 ✔
- 45 ✔
- 49 ✔
- 50 ✔
- 51 ✔
- 55 ✔
- 61 ✔
- 62 ✔
- 64 ✔
- 64 ✔
- 67 ✔
- 68 ✔
- 75 ✔
- 96 ✔
- 99 ✔
- 100 ✔
- 100 ✔

That’s 21 values. But wait — did we miss any?

Let’s go back to the original list:

Original:
50, 42, 100, 45, 68, 32, 100
67, 61, 31, 75, 39, 62, 64
49, 55, 51, 33, 99, 96, 64

Let’s list them one by one:

1. 50
2. 42
3. 100
4. 45
5. 68
6. 32
7. 100
8. 67
9. 61
10. 31
11. 75
12. 39
13. 62
14. 64
15. 49
16. 55
17. 51
18. 33
19. 99
20. 96
21. 64

Yes, 21 values.

Now sort them:

Sorted:
31, 32, 33, 39, 42, 45, 49, 50, 51, 55, 61, 62, 64, 64, 67, 68, 75, 96, 99, 100, 100

Wait — that’s 21? Let's count:

1. 31
2. 32
3. 33
4. 39
5. 42
6. 45
7. 49
8. 50
9. 51
10. 55
11. 61
12. 62
13. 64
14. 64
15. 67
16. 68
17. 75
18. 96
19. 99
20. 100
21. 100

Yes, correct.

Now count frequencies per interval.

---

Frequency Count

#### 31 - 40:
Temperatures between 31 and 40 inclusive:
31, 32, 33, 39 → 4 values
✔ Frequency = 4

#### 41 - 50:
42, 45, 49, 50 → 4 values
✔ Frequency = 4

#### 51 - 60:
51, 55 → 2 values
✔ Frequency = 2

#### 61 - 70:
61, 62, 64, 64, 67, 68 → 6 values
✔ Frequency = 6

#### 71 - 80:
75 → 1 value
✔ Frequency = 1

#### 81 - 90:
No values in this range
✔ Frequency = 0

#### 91 - 100:
96, 99, 100, 100 → 4 values
✔ Frequency = 4

---

✔ Final Frequency Table:

| Temperatures | Frequency |
|--------------|-----------|
| 31 - 40 | 4 |
| 41 - 50 | 4 |
| 51 - 60 | 2 |
| 61 - 70 | 6 |
| 71 - 80 | 1 |
| 81 - 90 | 0 |
| 91 - 100 | 4 |

---

Step 3: Draw the Histogram

Now, use the frequency table to draw a histogram.

#### How to draw it:

- X-axis: Temperature intervals (31–40, 41–50, ..., 91–100)
- Y-axis: Frequency (number of occurrences)

Each bar should represent one interval, with height equal to frequency.

#### Bar Heights:
- 31–40 → 4
- 41–50 → 4
- 51–60 → 2
- 61–70 → 6
- 71–80 → 1
- 81–90 → 0 (no bar or a very thin line)
- 91–100 → 4

You can draw the bars accordingly.

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✔ Summary Answer:

Frequency Table:

| Temperatures | Frequency |
|--------------|-----------|
| 31 - 40 | 4 |
| 41 - 50 | 4 |
| 51 - 60 | 2 |
| 61 - 70 | 6 |
| 71 - 80 | 1 |
| 81 - 90 | 0 |
| 91 - 100 | 4 |

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📊 Histogram Description:

- The x-axis has intervals: 31–40, 41–50, ..., 91–100.
- The y-axis goes from 0 to at least 6 (since max frequency is 6).
- Bars:
- 31–40: height 4
- 41–50: height 4
- 51–60: height 2
- 61–70: height 6
- 71–80: height 1
- 81–90: height 0 (no bar)
- 91–100: height 4

(You would draw this on the blank histogram grid provided.)

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🔍 Key Notes:

- Intervals are inclusive (e.g., 31–40 includes both 31 and 40).
- No gaps between bars in a histogram since it's continuous data.
- The histogram shows the distribution of temperature data.

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✔ You now have both the frequency table and the histogram ready!