Make less than orgive curve
Income: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Labour: 5, 15, 30, 50, 40, 20

To create a "less than ogive" curve, we first need to calculate cumulative frequencies for the given data. Here's how we do it step-by-step:

### Data Provided:
- **Income ranges (in thousands):** 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
- **Labor force in each range:** 5, 15, 30, 50, 40, 20

### Step 1: Calculate Cumulative Frequency
For a "less than ogive," cumulative frequencies are calculated by summing the labor force values sequentially.

| Income Range (in '000s) | Labor Force | Cumulative Frequency |
|-------------------------|-------------|----------------------|
| 0-10                    | 5           | 5                    |
| 10-20                   | 15          | 5 + 15 = 20          |
| 20-30                   | 30          | 20 + 30 = 50         |
| 30-40                   | 50          | 50 + 50 = 100        |
| 40-50                   | 40          | 100 + 40 = 140       |
| 50-60                   | 20          | 140 + 20 = 160       |

### Step 2: Plot the Ogive Curve
To plot the ogive, the x-axis will represent income ranges, and the y-axis will represent cumulative frequencies. Each point on the graph is plotted using the upper boundary of the income class and the cumulative frequency.

The points to plot will be:
- (10, 5)
- (20, 20)
- (30, 50)
- (40, 100)
- (50, 140)
- (60, 160)

This forms the cumulative curve for a "less than ogive."

Let me know if you'd like me to generate the actual graph or provide further clarification!

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### Further Related Questions:
1. How would you calculate the median from the less than ogive curve?
2. What is the difference between a "less than ogive" and a "greater than ogive"?
3. How would we use the ogive to estimate quartiles (Q1, Q3)?
4. Can you derive the percentage distribution from the given data?
5. What methods are there to calculate cumulative frequencies for different data sets?

### Tip:
When interpreting an ogive, the steepness of the curve indicates the concentration of data in particular income ranges!

Make less than ogive curve Income: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60 Labour: 5, 15, 30, 50, 40, 20

Learn how to create a less than ogive curve for income ranges (0-60) and corresponding labor force values. This solution walks through calculating cumulative frequency and plotting the ogive. Perfect for Grades 9-12 students learning about statistics and cumulative frequency.

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