Q.7) Draw the Box Plot for the Following Data.   [Draw using pencil only] 

  i) 60,65,78,85,92,103,120

To draw a box plot for the given data, we need to calculate a few key statistics: the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum values. Then, we use these statistics to create the box plot.

### Step-by-Step Solution:

Given dataTo draw a box plot for the given data, we need to calculate a few key statistics: the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum values. Then, we use these statistics to create the box plot.

### Step-by-Step Solution:

Given   
60, 65, 78, 85, 92, 103, 120

#### 1. Arrange the Data in Ascending Order:

The data is already sorted:  
60, 65, 78, 85, 92, 103, 120

#### 2. Find the Minimum and Maximum Values:

- Minimum (Min) = 60  
- Maximum (Max) = 120  

#### 3. Calculate the Median (Q2):

The median is the middle value of the ordered data. Since there are 7 data points (an odd number), the median is the 4th value.

- Median (Q2) = 85

#### 4. Calculate the Lower Quartile (Q1):

The lower quartile (Q1) is the median of the lower half of the data (excluding the overall median). The lower half is:  
60, 65, 78  

For these three values, the median (Q1) is the 2nd value.

- Lower Quartile (Q1) = 65

#### 5. Calculate the Upper Quartile (Q3):

The upper quartile (Q3) is the median of the upper half of the data (excluding the overall median). The upper half is:  
92, 103, 120  

For these three values, the median (Q3) is the 2nd value.

- Upper Quartile (Q3) = 103

#### 6. Construct the Box Plot:

To draw the box plot:

- Draw a number line that includes the range of the data (from 60 to 120).
- Plot the five key statistics: Min (60), Q1 (65), Median (85), Q3 (103), and Max (120).
- Draw a box from Q1 (65) to Q3 (103) and a line at the median (85).
- Draw "whiskers" from Q1 to the Min (60) and from Q3 to the Max (120).

### Box Plot Summary:

- **Min**: 60  
- **Q1**: 65  
- **Median (Q2)**: 85  
- **Q3**: 103  
- **Max**: 120  

Would you like to know more about how to interpret this box plot or any other statistics topic? 

Here are 5 related questions:
1. How do you calculate the interquartile range (IQR) from a box plot?
2. What do outliers represent in a box plot, and how are they calculated?
3. How can you compare multiple box plots to understand the distribution differences?
4. What are the limitations of using a box plot for data visualization?
5. How can box plots be used in real-world data analysis?

**Tip**: When interpreting a box plot, always check for the spread of the data and any potential outliers. This can provide insights into the data's variability and skewness.

Q.7) Draw the Box Plot for the Following Data. [Draw using pencil only] i) 60,65,78,85,92,103,120

Learn how to construct a box plot for the data set 60, 65, 78, 85, 92, 103, 120 with a step-by-step guide. This example covers key statistics concepts like quartiles and medians. Suitable for students in Grades 7-9.

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