The following table gives the lifetime of 400 neon lamps.
| lifetime in hours | No. of lamps |
|---|---|
| [tex]$300-400$[/tex] | 14 |
| [tex]$400-500$[/tex] | 56 |
| [tex]$500-600$[/tex] | 60 |
| [tex]$600-700$[/tex] | 86 |
| [tex]$700-800$[/tex] | 74 |
| [tex]$800-900$[/tex] | 62 |
| [tex]$900-1000$[/tex] | 48 |
Represent given info with the help of a histogram.
Answer (2)
We create a histogram to represent the lifetime of neon lamps by plotting intervals on the x-axis and the number of lamps on the y-axis. Each bar's height corresponds to the number of lamps in that lifetime interval, visually displaying the distribution of lamp durations. This helps us analyze which ranges have the highest frequency among the lamp lifetimes.
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The problem requires representing the lifetime of neon lamps using a histogram.
The x-axis represents the lifetime intervals (300-400, 400-500, ..., 900-1000), and the y-axis represents the number of lamps in each interval.
Each interval is represented by a bar with a height corresponding to the number of lamps in that interval.
The histogram visually displays the distribution of lamp lifetimes.
Explanation
Understand the problem and provided data We are given a table that shows the lifetime of 400 neon lamps, grouped into intervals of 100 hours. Our goal is to represent this data using a histogram. A histogram is a graphical representation of data that groups data points into specified ranges (intervals). The x-axis represents the intervals (lifetime in hours), and the y-axis represents the frequency (number of lamps) in each interval.
Identify the data for each interval To create the histogram, we'll draw bars for each interval. The height of each bar corresponds to the number of lamps in that interval.
Interval 300-400: 14 lamps
Interval 400-500: 56 lamps
Interval 500-600: 60 lamps
Interval 600-700: 86 lamps
Interval 700-800: 74 lamps
Interval 800-900: 62 lamps
Interval 900-1000: 48 lamps
Define the axes The x-axis will represent the lifetime in hours, with intervals: 300-400, 400-500, 500-600, 600-700, 700-800, 800-900, and 900-1000. The y-axis will represent the number of lamps.
Draw the histogram bars For each interval on the x-axis, we draw a bar with a height corresponding to the number of lamps on the y-axis. For example, for the interval 300-400, the height of the bar will be 14.
Final Answer The histogram visually represents the distribution of the lifetime of the neon lamps. The height of each bar shows how many lamps fall into each lifetime interval.
Examples
Histograms are used in various real-life scenarios, such as analyzing the distribution of exam scores in a class, representing the frequency of different age groups in a population, or visualizing the distribution of heights or weights in a sample. In this case, we use a histogram to understand the distribution of the lifetime of neon lamps, which can help manufacturers assess the quality and durability of their products.
