ben and glen are practicing short golf shots. they are aiming for a flag that is 110 yards away? they consider any shot between 105 and 115 yards to be accurate. here are their results in yards. ben: 110,130,88,105,108,110,118,100,120,103.and Glen: 95,105,108,110,106,110,108,100,118,105. make a data display that makes it easy to see how the data for each set of golf shots is distributed. how successful were each of them in hitting accurate shots? how does your data display show this?
To make a data display that shows the distribution of data for each set of golf shots, we can create a histogram. In a histogram, the X-axis represents the range of values, and the Y-axis represents the frequency or number of occurrences.
For this specific case, we will create separate histograms for Ben's and Glen's shots. The X-axis will represent the shot distances, and the Y-axis will represent the frequency of shots in each distance range.
Here is how you can create the histograms step by step:
1. First, list down the range of shot distances. In this case, we can start with 85 and increment by 5 until 120.
Range: 85, 90, 95, 100, 105, 110, 115, 120
2. Count the frequency or number of shots that fall within each distance range for both Ben and Glen.
Ben's Shots:
- 85-90: 0
- 90-95: 0
- 95-100: 2
- 100-105: 1
- 105-110: 3
- 110-115: 2
- 115-120: 2
Glen's Shots:
- 85-90: 0
- 90-95: 1
- 95-100: 2
- 100-105: 2
- 105-110: 3
- 110-115: 0
- 115-120: 2
3. Draw a histogram for Ben's and Glen's shots separately, using the frequency data.
Ben's Shots:
------------
| . . . X |
| X |
| X X |
| X . X |
| X . |
| X . X . X X |
|_____________|
95 100 105 110 115 120
Glen's Shots:
------------
| X |
| X X |
| X X X |
| X . X |
| X . . X X |
|_____________|
95 100 105 110 115 120
The histograms provide a visual representation of the distribution of shots for each player. Each "X" represents a shot falling into that distance range, and the height of the bars represents the frequency of shots in that range.
Analyzing the histograms, we can determine how successful each player was in hitting accurate shots:
Ben's Accuracy:
Ben had the most shots falling within the accurate range of 105-115 yards. He had a total of 7 shots in this range out of 10 shots, making him more successful. The histogram displays a higher bar in the 105-110 range, indicating that he was consistently hitting shots closer to the target.
Glen's Accuracy:
Glen had 5 shots falling within the accurate range of 105-115 yards, which is only half of his total shots. The histogram for Glen shows a more varied distribution, and although he had a few shots near the accurate range, he was less consistent compared to Ben.
In summary, Ben was more successful in hitting accurate shots, as indicated by a higher number of shots within the desired range and a more concentrated distribution on the histogram. Glen had a less consistent performance, with a wider spread of shots.