Questions: Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was won 10-14 15-19 20-24 25-29 30-34 35-39 40-44 Identify the upper class limits. 14, 19, 24, 29, 34, 39, 44 Identify the class width. 5 Identify the class midpoints. 12.0, 17.0, 22.0, 27.0, 32.0, 37.0, 42.0 Identify the class boundaries.

Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was won 10-14 15-19 20-24 25-29 30-34 35-39 40-44 Identify the upper class limits. 14, 19, 24, 29, 34, 39, 44 Identify the class width. 5 Identify the class midpoints. 12.0, 17.0, 22.0, 27.0, 32.0, 37.0, 42.0 Identify the class boundaries.
Transcript text: Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was wor 10-14 $15-19$ $20-24$ 25-29 30-34 35-39 $40-44$ Identify the upper class limits. \[ 14,19,24,29,34,39,44 \] Identify the class width. 5 Identify the class midpoints. \[ 12.0,17.0,22.0,27.0,32.0,37.0,42.0 \] Identify the class boundaries. $\square$ ,$\square$, $\square$ $\square$ $\square$ $\square$ $\square$ $\square$
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Solution

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Solution Steps

To solve this problem, we need to identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. We will also determine the number of individuals included in the summary.

  1. Lower Class Limits: These are the smallest values that can belong to each class.
  2. Upper Class Limits: These are the largest values that can belong to each class.
  3. Class Width: This is the difference between the lower limits of consecutive classes.
  4. Class Midpoints: These are the averages of the lower and upper class limits.
  5. Class Boundaries: These are the values that separate the classes without gaps.
Step 1: Identify the Lower Class Limits

The lower class limits are the smallest values that can belong to each class. From the given data: \[ \text{Lower Class Limits} = [10, 15, 20, 25, 30, 35, 40] \]

Step 2: Identify the Upper Class Limits

The upper class limits are the largest values that can belong to each class. From the given data: \[ \text{Upper Class Limits} = [14, 19, 24, 29, 34, 39, 44] \]

Step 3: Calculate the Class Width

The class width is the difference between the lower limits of consecutive classes: \[ \text{Class Width} = 15 - 10 = 5 \]

Step 4: Calculate the Class Midpoints

The class midpoints are the averages of the lower and upper class limits: \[ \text{Class Midpoints} = \left[ \frac{10 + 14}{2}, \frac{15 + 19}{2}, \frac{20 + 24}{2}, \frac{25 + 29}{2}, \frac{30 + 34}{2}, \frac{35 + 39}{2}, \frac{40 + 44}{2} \right] = [12.0, 17.0, 22.0, 27.0, 32.0, 37.0, 42.0] \]

Step 5: Calculate the Class Boundaries

The class boundaries are the values that separate the classes without gaps. They are calculated as follows: \[ \text{Class Boundaries} = [(10 - 0.5, 14 + 0.5), (15 - 0.5, 19 + 0.5), (20 - 0.5, 24 + 0.5), (25 - 0.5, 29 + 0.5), (30 - 0.5, 34 + 0.5), (35 - 0.5, 39 + 0.5), (40 - 0.5, 44 + 0.5)] \] \[ = [(9.5, 14.5), (14.5, 19.5), (19.5, 24.5), (24.5, 29.5), (29.5, 34.5), (34.5, 39.5), (39.5, 44.5)] \]

Final Answer

\[ \boxed{ \begin{aligned} &\text{Lower Class Limits:} & [10, 15, 20, 25, 30, 35, 40] \\ &\text{Upper Class Limits:} & [14, 19, 24, 29, 34, 39, 44] \\ &\text{Class Width:} & 5 \\ &\text{Class Midpoints:} & [12.0, 17.0, 22.0, 27.0, 32.0, 37.0, 42.0] \\ &\text{Class Boundaries:} & [(9.5, 14.5), (14.5, 19.5), (19.5, 24.5), (24.5, 29.5), (29.5, 34.5), (34.5, 39.5), (39.5, 44.5)] \\ &\text{Number of Individuals:} & \text{Not provided} \end{aligned} } \]

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