The table gives information about the lengths of time, in hours, some children spent watching TV last week.
| Length of time $(t)$ | Frequency |
| :--------------------- | :-------- |
| $0 \leqslant t<10$ | 8 |
| $10 \leqslant t<15$ | 15 |
| $15 \leqslant t<20$ | 10 |
| $20 \leqslant t<30$ | 11 |
Draw a histogram for the information in the table.
Answer (1)
Calculate the class widths for each interval.
Calculate the frequency density for each interval using the formula: Frequency Density = Frequency / Class Width.
Draw the histogram with time (t) on the x-axis and frequency density on the y-axis.
The height of each bar will represent the frequency density for the corresponding interval, and the width of each bar will represent the class width.
Explanation
Understanding the Problem We are given a frequency table that shows the time children spent watching TV. Our goal is to draw a histogram to represent this data. To do this, we need to calculate the frequency density for each class interval. Frequency density is calculated as Frequency / Class Width.
Calculating Class Widths First, we calculate the class widths for each interval:
Interval 1: 0 ≤ t < 10 , Class Width = 10 − 0 = 10
Interval 2: 10 ≤ t < 15 , Class Width = 15 − 10 = 5
Interval 3: 15 ≤ t < 20 , Class Width = 20 − 15 = 5
Interval 4: 20 ≤ t < 30 , Class Width = 30 − 20 = 10
Calculating Frequency Densities Next, we calculate the frequency densities for each interval:
Interval 1: Frequency Density = 10 8 = 0.8
Interval 2: Frequency Density = 5 15 = 3
Interval 3: Frequency Density = 5 10 = 2
Interval 4: Frequency Density = 10 11 = 1.1
Drawing the Histogram Now we have all the information needed to draw the histogram. The x-axis will represent the time intervals, and the y-axis will represent the frequency density. Each bar's height corresponds to the frequency density of its interval, and the bar's width corresponds to the class width.
Examples
Histograms are used in many real-world scenarios, such as analyzing the distribution of exam scores in a class, visualizing the distribution of income levels in a population, or representing the frequency of different types of defects in a manufacturing process. In this case, we use a histogram to visualize the distribution of time spent watching TV by children.
