The accompanying relative frequency ogive represents the composite score on a standardized test for a high school graduating class. Complete parts (a) through (d) below. Click the icon to view the ogive. (a) What is the class width? (Type a whole number.) (b) Approximately 25% of students had a composite score below what level? (Type a whole number.) (c) What percentage of students had a composite score less than 24? (Type a whole number.) (d) Five percent of students had a composite score above what level? (Type a whole number.)

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The accompanying relative frequency ogive represents the composite score on a standardized test for a high school graduating class. Complete parts (a) through (d) below.

[Click the icon to view the ogive.]

(a) What is the class width?
   [ ] (Type a whole number.)

(b) Approximately 25% of students had a composite score below what level?
   [ ] (Type a whole number.)

(c) What percentage of students had a composite score less than 24?
   [ ]% (Type a whole number.)

(d) Five percent of students had a composite score above what level?
   [ ] (Type a whole number.)
Transcribed Image Text:The accompanying relative frequency ogive represents the composite score on a standardized test for a high school graduating class. Complete parts (a) through (d) below. [Click the icon to view the ogive.] (a) What is the class width? [ ] (Type a whole number.) (b) Approximately 25% of students had a composite score below what level? [ ] (Type a whole number.) (c) What percentage of students had a composite score less than 24? [ ]% (Type a whole number.) (d) Five percent of students had a composite score above what level? [ ] (Type a whole number.)
**Ogive of Composite Scores**

The graph provided is an ogive (cumulative frequency graph) of composite scores. An ogive is a useful tool for understanding the cumulative distribution of data points.

### Detailed Explanation of the Graph

#### Axes:
1. **X-axis (Horizontal):** The x-axis represents the composite scores, ranging from 0 to 36.
2. **Y-axis (Vertical):** The y-axis represents the cumulative relative frequency, ranging from 0 to 1 (or 0% to 100%).

#### Data Points:
- The data points are plotted as black dots, with a blue line connecting them, creating a smooth curve.
- The curve starts at the origin (0,0) and rises as it moves to the right.
- Initially, there is a slow increase in cumulative relative frequency for lower composite scores (0-6).
- There is a noticeable sharp rise in cumulative relative frequency as composite scores increase from around 8 to 24.
- The curve levels off once composite scores exceed 30, suggesting the majority of data points are within this range (30-36).

#### Interpretation:
- The cumulative relative frequency is the sum of the frequencies of scores up to a certain point.
- For lower composite scores (around 0-8), the cumulative relative frequency is low, indicating fewer data points achieve these scores.
- As the composite scores increase (8-24), the cumulative relative frequency rapidly increases, reflecting many data points achieving these mid-range scores.
- The flattening of the curve for composite scores above 30 indicates that most data points have been accounted for by this stage, and relatively few data points achieve the upper end of the range (30-36).

### Educational Insights
An ogive provides insights into how data accumulates across a range of values and helps visualize the distribution's cumulative aspect. In educational contexts, this can help in:
- Understanding how scores are distributed across a test or assessment.
- Identifying thresholds or benchmarks (e.g., what score corresponds to the top 25% of test-takers).
- Analyzing the distribution pattern to assess overall performance trends.

Understanding and interpreting ogives are essential skills in data analysis and statistics. They emphasize cumulative aspects and are often used alongside histograms or other frequency distribution charts for comprehensive data exploration.
Transcribed Image Text:**Ogive of Composite Scores** The graph provided is an ogive (cumulative frequency graph) of composite scores. An ogive is a useful tool for understanding the cumulative distribution of data points. ### Detailed Explanation of the Graph #### Axes: 1. **X-axis (Horizontal):** The x-axis represents the composite scores, ranging from 0 to 36. 2. **Y-axis (Vertical):** The y-axis represents the cumulative relative frequency, ranging from 0 to 1 (or 0% to 100%). #### Data Points: - The data points are plotted as black dots, with a blue line connecting them, creating a smooth curve. - The curve starts at the origin (0,0) and rises as it moves to the right. - Initially, there is a slow increase in cumulative relative frequency for lower composite scores (0-6). - There is a noticeable sharp rise in cumulative relative frequency as composite scores increase from around 8 to 24. - The curve levels off once composite scores exceed 30, suggesting the majority of data points are within this range (30-36). #### Interpretation: - The cumulative relative frequency is the sum of the frequencies of scores up to a certain point. - For lower composite scores (around 0-8), the cumulative relative frequency is low, indicating fewer data points achieve these scores. - As the composite scores increase (8-24), the cumulative relative frequency rapidly increases, reflecting many data points achieving these mid-range scores. - The flattening of the curve for composite scores above 30 indicates that most data points have been accounted for by this stage, and relatively few data points achieve the upper end of the range (30-36). ### Educational Insights An ogive provides insights into how data accumulates across a range of values and helps visualize the distribution's cumulative aspect. In educational contexts, this can help in: - Understanding how scores are distributed across a test or assessment. - Identifying thresholds or benchmarks (e.g., what score corresponds to the top 25% of test-takers). - Analyzing the distribution pattern to assess overall performance trends. Understanding and interpreting ogives are essential skills in data analysis and statistics. They emphasize cumulative aspects and are often used alongside histograms or other frequency distribution charts for comprehensive data exploration.
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