Fillable Online Frequency and Data Distribution Guided Lesson ... - Free Printable

Thank you for uploading the image. It contains a “Frequency and Data Distribution – Guided Lesson” worksheet with three questions. I’ll solve each question step by step and explain the reasoning.

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## 📌 Question 1: Draw a bar graph to represent this data.

> Data:
> 51 63 45 38 50 54 44 57 41 48 31 44
> 58 40 54 65 39 27 22 56 38 45 70 60
> 30 37 56 74 52 28 50 28 47 25 60 61
> 38 32 65 42

✔ Step-by-Step Solution:

Step 1: Organize the data (optional but helpful)
Sort the data to see patterns, though not required for bar graph.

But since it’s a bar graph, we need to decide what to put on the x-axis and y-axis.

👉 In most cases, for raw data like this, we create a frequency distribution first — group the data into intervals (bins), then count how many scores fall into each interval.

Let’s make intervals of 10:

- 20–29
- 30–39
- 40–49
- 50–59
- 60–69
- 70–79

Step 2: Count frequency in each interval

Let’s go through the data:

- 20–29: 27, 22, 28, 28, 25 → 5
- 30–39: 38, 31, 39, 30, 37, 38, 38, 32 → 8
- 40–49: 45, 44, 41, 48, 44, 40, 45, 47, 42 → 9
- 50–59: 51, 50, 54, 57, 58, 54, 56, 56, 52, 50 → 10
- 60–69: 63, 65, 60, 60, 61, 65 → 6
- 70–79: 70, 74 → 2

✔ So, frequencies are:
- 20–29: 5
- 30–39: 8
- 40–49: 9
- 50–59: 10
- 60–69: 6
- 70–79: 2

Step 3: Draw the bar graph

You would draw:

- X-axis: labeled with intervals (20–29, 30–39, etc.)
- Y-axis: frequency (from 0 to 10 or 11)
- Bars: height = frequency for each interval

> 🖍️ *Since I can’t draw here, imagine a bar graph where the tallest bar is 50–59 (height=10), then 40–49 (9), then 30–39 (8), etc.*

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## 📌 Question 2: The grocer measures the weight of mangoes (in grams). Use a line graph to represent this data.

> Data:
> 45 50 44 57 44 49 27 22 56 38 60
> 30 37 56 74 50 28 60 61 32

✔ Step-by-Step Solution:

A line graph is typically used to show trends over time or ordered categories. Since no time or order is given, we assume the data is listed in order (e.g., mango #1 to #20).

So, we plot:

- X-axis: Mango number (1 to 20)
- Y-axis: Weight (grams)

Then connect the points with lines.

Step 1: List data with index

| Mango # | Weight (g) |
|---------|------------|
| 1 | 45 |
| 2 | 50 |
| 3 | 44 |
| 4 | 57 |
| 5 | 44 |
| 6 | 49 |
| 7 | 27 |
| 8 | 22 |
| 9 | 56 |
| 10 | 38 |
| 11 | 60 |
| 12 | 30 |
| 13 | 37 |
| 14 | 56 |
| 15 | 74 |
| 16 | 50 |
| 17 | 28 |
| 18 | 60 |
| 19 | 61 |
| 20 | 32 |

Step 2: Plot points and connect

You’d plot each point (1,45), (2,50), ..., (20,32) and connect them with straight lines.

> 🖍️ *Again, I can’t draw, but imagine a jagged line going up and down — starting at 45, jumping to 50, dipping to 22, spiking to 74, etc.*

This shows variation in mango weights.

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## 📌 Question 3: Use a frequency distribution to determine the median and mode of the data.

Same data as Question 1:

> 51 63 45 38 50 54 44 57 41 48 31 44
> 58 40 54 65 39 27 22 56 38 45 70 60
> 30 37 56 74 52 28 50 28 47 25 60 61
> 38 32 65 42

✔ Step 1: Find the Mode

Mode = most frequently occurring value.

Let’s count frequency of each score:

We’ll list unique values and count:

- 22: 1
- 25: 1
- 27: 1
- 28: 2
- 30: 1
- 31: 1
- 32: 1
- 37: 1
- 38: 3 ← ✔ Most frequent!
- 39: 1
- 40: 1
- 41: 1
- 42: 1
- 44: 2
- 45: 2
- 47: 1
- 48: 1
- 49: 1
- 50: 2
- 51: 1
- 52: 1
- 54: 2
- 56: 2
- 57: 1
- 58: 1
- 60: 2
- 61: 1
- 63: 1
- 65: 2
- 70: 1
- 74: 1

✔ Mode = 38 (appears 3 times — more than any other)

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✔ Step 2: Find the Median

Median = middle value when data is sorted.

Total number of data points = 4 rows × 12 = 48 values

Since 48 is even, median = average of 24th and 25th values.

Step 2a: Sort the data

Sorted data (ascending):

22, 25, 27, 28, 28, 30, 31, 32, 37, 38, 38, 38,
39, 40, 41, 42, 44, 44, 45, 45, 47, 48, 49, 50,
50, 51, 52, 54, 54, 56, 56, 57, 58, 60, 60, 61,
63, 65, 65, 70, 74

Let’s count to find 24th and 25th:

Positions 1–12:
22, 25, 27, 28, 28, 30, 31, 32, 37, 38, 38, 38 → position 12 = 38

Positions 13–24:
39, 40, 41, 42, 44, 44, 45, 45, 47, 48, 49, 50 → position 24 = 50

Position 25: next value = 50

✔ So, median = (50 + 50) / 2 = 50

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## ✔ Final Answers:

Question 1: Bar Graph

- Group data into intervals (20–29, 30–39, etc.)
- Frequencies: [5, 8, 9, 10, 6, 2]
- Draw bars accordingly.

Question 2: Line Graph

- Plot mango number (1–20) vs. weight (grams)
- Connect points with lines to show variation.

Question 3: Median and Mode

- Mode = 38 (appears 3 times)
- Median = 50 (average of 24th and 25th values in sorted list)

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✔ You’re all set! Let me know if you want help drawing these graphs manually or digitally.