# Given Information - Class Intervals and Frequencies: - –10: 6 - 10–20: ? - 20–30: 14 - 30–40: 10 - Total frequency = 40 # What Have to Find - The missing frequency for the class interval 10–20. - Draw the histogram for the data. # Definition or Concept Used - **Frequency**: The number of observations in each class interval. - **Histogram**: A graphical representation of data using bars of different heights. The height of each bar shows the frequency of each class interval. - **Total Frequency**: The sum of all class frequencies should equal the given total frequency. # Solution Let the missing frequency for the class interval 10–20 be \( x \). Sum of all frequencies is given as 40. So, \[ 6 + x + 14 + 10 = 40 \] \[ 6 + x + 24 = 40 \] \[ x + 30 = 40 \] \[ x = 40 - 30 \] \[ x = 10 \] So, the missing frequency is 10. The complete frequency table is: | Class | Frequency | |---------|-----------| | –10 | 6 | | 10–20 | 10 | | 20–30 | 14 | | 30–40 | 10 | Now, draw the histogram using these frequencies. --- ### Histogram - Draw X-axis (Class Intervals: –10, 10–20, 20–30, 30–40) - Draw Y-axis (Frequency: scale up to at least 14) - For each class interval, draw a bar up to the corresponding frequency.  *Alt text: Histogram showing bars for class intervals –10 (6), 10–20 (10), 20–30 (14), 30–40 (10).* # Summary - Missing frequency for 10–20 is **10**. - Histogram is drawn with frequencies: 6, 10, 14, 10.

# Given Information - Class Intervals and Frequencies: - 0–10: 6 - 10–20: ? - 20–30: 14 - 30–40: 10 - Total Frequency = 40 # What Have to Find - The missing frequency for the class interval 10–20. - A histogram representing the data. # Definition or Concept Used - **Frequency**: The count of occurrences within each class interval. - **Histogram**: A bar graph that shows the distribution of numerical data, where each bar represents a class interval and its height corresponds to the frequency. - **Total Frequency**: The cumulative sum of all class interval frequencies, which should equal the stated total frequency. # Solution Let the missing frequency for the class interval 10–20 be denoted as \( x \). To find \( x \), we set up the equation based on the total frequency: \[ 6 + x + 14 + 10 = 40 \] Simplifying the equation: \[ 6 + x + 24 = 40 \] \[ x + 30 = 40 \] \[ x = 40 - 30 \] \[ x = 10 \] The missing frequency is 10. The completed frequency table is as follows: | Class | Frequency | |---------|-----------| | 0–10 | 6 | | 10–20 | 10 | | 20–30 | 14 | | 30–40 | 10 | Next, we can construct the histogram using the provided frequencies. ### Steps to Draw the Histogram - **X-axis**: Label with Class Intervals (0–10, 10–20, 20–30, 30–40). - **Y-axis**: Label with Frequency, ensuring the scale reaches at least 14. - **Bars**: For each class interval, draw a bar corresponding to its frequency: - 0–10: Height of 6 - 10–20: Height of 10 - 20–30: Height of 14 - 30–40: Height of 10  *Alt text: Histogram illustrating class intervals with respective frequencies: 0–10 (6), 10–20 (10), 20–30 (14), 30–40 (10).* # Summary - Missing frequency for the class interval 10–20 is **10**. - The histogram has been drawn with the frequencies: 6, 10, 14, 10.

# Given Information - Class Intervals and Frequencies: - 0–10: 6 - 10–20: ? - 20–30: 14 - 30–40: 10 - Total Frequency = 40 # What Needs to be Found - The unknown frequency for the class interval 10–20. - A histogram to visualize the data. # Definition or Concept Used - **Frequency**: The number of data points that fall within a specified class interval. - **Histogram**: A type of bar chart representing the distribution of numerical data, where each bar's height reflects the frequency of the corresponding class interval. - **Total Frequency**: The sum of all individual frequencies, which should equal the provided total frequency. # Solution Let the unknown frequency for the class interval 10–20 be represented as \( x \). To determine \( x \), we can formulate an equation based on the total frequency: \[ 6 + x + 14 + 10 = 40 \] Rearranging and simplifying gives: \[ 6 + x + 24 = 40 \] \[ x + 30 = 40 \] \[ x = 40 - 30 \] \[ x = 10 \] Thus, the missing frequency is 10. The complete frequency table is: | Class | Frequency | |---------|-----------| | 0–10 | 6 | | 10–20 | 10 | | 20–30 | 14 | | 30–40 | 10 | Next, we will create the histogram based on the frequencies obtained. ### Steps to Draw the Histogram - **X-axis**: Label it with the Class Intervals (0–10, 10–20, 20–30, 30–40). - **Y-axis**: Label it with Frequency, ensuring it can accommodate values up to at least 14. - **Bars**: Construct bars for each class interval according to their frequencies: - 0–10: Bar height of 6 - 10–20: Bar height of 10 - 20–30: Bar height of 14 - 30–40: Bar height of 10  *Alt text: Histogram depicting class intervals and their corresponding frequencies: 0–10 (6), 10–20 (10), 20–30 (14), 30–40 (10).* # Summary - The missing frequency for the 10–20 class interval is **10**. - The histogram has been completed with the following frequencies: 6, 10, 14, 10.

# Given Information - Class Intervals and Corresponding Frequencies: - 0–10: 6 - 10–20: ? - 20–30: 14 - 30–40: 10 - Total Frequency = 40 # What Needs to be Determined - The frequency for the class interval 10–20, which is currently unknown. - A histogram based on the provided frequencies. # Definition or Concept Used - **Frequency**: The count of occurrences for each specified class interval. - **Histogram**: A graphical representation of data, where each bar indicates the frequency of a particular class interval. - **Total Frequency**: The sum of all frequencies, which should equal the specified total frequency. # Solution Let the unknown frequency for the class interval 10–20 be denoted as \( x \). To find \( x \), we can set up the equation based on the total frequency: \[ 6 + x + 14 + 10 = 40 \] Simplifying the equation gives: \[ 6 + x + 24 = 40 \] \[ x + 30 = 40 \] \[ x = 40 - 30 \] \[ x = 10 \] Therefore, the missing frequency is 10. The completed frequency table is as follows: | Class | Frequency | |---------|-----------| | 0–10 | 6 | | 10–20 | 10 | | 20–30 | 14 | | 30–40 | 10 | Next, we will create a histogram based on these frequencies. ### Steps to Create the Histogram - **X-axis**: Label with Class Intervals (0–10, 10–20, 20–30, 30–40). - **Y-axis**: Label with Frequency, ensuring it can reach at least 14. - **Bars**: Draw bars for each class interval reflecting the respective frequencies: - 0–10: Height of 6 - 10–20: Height of 10 - 20–30: Height of 14 - 30–40: Height of 10  *Alt text: Histogram illustrating class intervals and their frequencies: 0–10 (6), 10–20 (10), 20–30 (14), 30–40 (10).* # Summary - The frequency for the class interval 10–20 is **10**. - The histogram has been constructed with the frequencies: 6, 10, 14, 10.