I do not get how to do this question, can you explain it?---**Problem Number:** 8
**Question Stem:**
Three different electric sensors, A, B and C, are used to detect movement in Harvey's backyard over a period of 3 weeks. An in-built device counts the number of times the sensor detects movement each night. The results are as follows.
**Table:**
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
|------------|---|----|---|---|----|----|---|---|---|----|----|----|----|----|----|----|----|----|----|----|----|
| Sensor A | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| Sensor B | 0 | 15 | 1 | 2 | 18 | 20 | 2 | 1 | 3 | 25 | 0 | 0 | 1 | 15 | 8 | 9 | 0 | 0 | 2 | 23 | 2 |
| Sensor C | 4 | 6 | 8 | 3 | 5 | 5 | 5 | 4 | 8 | 2 | 3 | 3 | 1 | 2 | 2 | 1 | 5 | 4 | 0 | 4 | 9 |
**Sub-questions:**
a Using class intervals of 3 and starting at 0, draw up a frequency table for each sensor.
b Draw histograms for each sensor.
c Given that it is known that stray cats consistently wander into Harvey's backyard, how would you describe the performance of:
i sensor A?
ii sensor B?
iii sensor C?
**Image Description:**
Type: Photograph.
Main Elements: A small possum-like animal is shown on the ground, surrounded by dry leaves, branches, and some green vegetation in the background. The animal is facing slightly to the left, looking towards the front, with its mouth slightly open and tongue visible. It appears to be sniffing or eating something on the ground.
Caption: Possums could set off the sensors.
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Let's analyze this motion sensor problem step by step. Harvey has three different sensors A, B, and C monitoring his backyard for 21 nights. We know that stray cats consistently wander into the area. Looking at the data table, we can see very different patterns for each sensor. Sensor A shows mostly zeros with occasional low counts. Sensor B has highly variable readings with some very high spikes. Sensor C shows more consistent moderate values. Our task is to create frequency tables and histograms to better understand each sensor's performance.
Now let's create frequency tables for each sensor. We use class intervals of 3 starting at 0, giving us intervals from 0 to 3, 3 to 6, and so on up to 24 to 27. For each sensor, we count how many nights fall into each interval. Sensor A has 21 nights in the 0 to 3 range and zero in all other ranges, showing very low detection counts. Sensor B shows a spread across multiple intervals with 12 nights in the lowest range but also activity in higher ranges including the highest intervals. Sensor C has 6 nights in the lowest range, 11 nights in the 3 to 6 range, and decreasing frequencies in higher ranges, showing more moderate and consistent detection patterns.
Now let's visualize this data with histograms. Each histogram shows the number of nights on the vertical axis and detection intervals on the horizontal axis. Sensor A's histogram shows a single tall bar at the zero to three interval with 21 nights, indicating it rarely detects movement. Sensor B's histogram is spread across many intervals, showing high variability with bars in both low and high detection ranges. Sensor C's histogram shows most activity in the three to six range with 11 nights, and decreasing frequency in higher ranges, suggesting consistent moderate detection levels. These visual patterns will help us evaluate each sensor's performance.
Now let's analyze each sensor's performance given that stray cats consistently wander into the backyard. Sensor A shows poor performance with zero detections on 14 out of 21 nights and a maximum of only 2 detections. This suggests it's not sensitive enough to reliably detect the expected cat activity. Sensor B shows inconsistent performance with highly variable readings from 0 to 25 detections. While it does detect activity, the extremely high counts suggest it may be overly sensitive or detecting false triggers. Sensor C demonstrates the most reliable performance with consistent moderate detection counts, mostly between 3 and 6 per night. This pattern aligns well with what we'd expect from regular cat activity. Therefore, Sensor C appears to be the most effective for this application.
To summarize what we've learned: We used frequency tables and histograms to analyze motion sensor data. Frequency tables help organize data into meaningful intervals, while histograms provide clear visual patterns. Our analysis revealed that Sensor A underperformed with too few detections, Sensor B was inconsistent and overly sensitive, while Sensor C provided the most reliable performance for detecting consistent animal activity like stray cats.