Student Heights Histogram: Analysis And Calculation

Oct 17, 2025 by Dimemap Team 52 views

Let's dive into analyzing this histogram of student heights, guys! We're going to figure out how many students fall within a specific height range and calculate the percentage of students within another range. Histograms are super useful for visualizing data, and in this case, we're using it to understand the distribution of student heights. Understanding histograms is essential for data interpretation, whether you're a student, a researcher, or just someone curious about statistics. This exercise will walk you through extracting meaningful information from a histogram, enhancing your ability to analyze and interpret data effectively. So, let's put on our thinking caps and get started!

Understanding the Histogram

Before we jump into the questions, let's make sure we all understand what a histogram is showing us. A histogram is a graphical representation of data that groups data points into ranges (also called bins) and uses bars to represent the number of data points in each range. The height of each bar corresponds to the frequency or count of data points within that range. In our case, the x-axis represents the heights of the students in centimeters, and the y-axis represents the number of students. Each bar shows how many students fall within a specific height range. For example, if there's a bar between 140 cm and 150 cm, the height of that bar tells us how many students have heights in that range. Now, let's tackle the questions using the information presented in the histogram.

a) How many students are between 140 cm and 160 cm?

To figure this out, we need to look at the bars that represent the height ranges between 140 cm and 160 cm. Typically, a histogram will have bars representing ranges like 140-150 cm and 150-160 cm. We need to read the height of each of these bars to find out how many students are in each range. Let's say the histogram shows the following:

The bar for 140-150 cm has a height of 20 students.
The bar for 150-160 cm has a height of 30 students.

To find the total number of students between 140 cm and 160 cm, we simply add the number of students in each range:

20 students (140-150 cm) + 30 students (150-160 cm) = 50 students

So, there are a total of 50 students who measure between 140 cm and 160 cm. Remember, the key here is to accurately read the height of each bar and sum the values for the specified ranges. This simple addition gives us the total count of students within the given height interval. Make sure to double-check the histogram to get the correct values for each bar height. Knowing how to read and interpret this data is super important for understanding the distribution of student heights.

b) What percentage of students measure more than 130 cm but less than 170 cm?

Okay, so this is where things get a little more interesting, but don't worry, we got this! To find the percentage of students who measure more than 130 cm but less than 170 cm, we need a few pieces of information:

The number of students in each height range between 130 cm and 170 cm.
The total number of students.

Let's break it down step by step. First, identify the relevant bars in the histogram. We're looking for the bars that cover the ranges between 130 cm and 170 cm. This might include ranges like 130-140 cm, 140-150 cm, 150-160 cm, and 160-170 cm. Read the height of each bar to find the number of students in each range. For example:

130-140 cm: 25 students
140-150 cm: 20 students
150-160 cm: 30 students
160-170 cm: 15 students

Next, add up the number of students in all these ranges to find the total number of students between 130 cm and 170 cm:

25 + 20 + 30 + 15 = 90 students

Now, we need to know the total number of students in the entire group. To find this, you'd need to add up the heights of all the bars in the histogram, not just the ones between 130 cm and 170 cm. Let's say, for example, that after adding up all the bars, we find that there are a total of 150 students.

Finally, to find the percentage, we use the formula:

(Number of students between 130 cm and 170 cm / Total number of students) * 100

So, in our example:

(90 / 150) * 100 = 60%

Therefore, 60% of the students measure more than 130 cm but less than 170 cm. Remember, the key to getting this right is to accurately read the histogram, sum the relevant values, and then apply the percentage formula. Always double-check your calculations to make sure you haven't made any errors. This kind of problem is super common in statistics, so mastering it now will definitely pay off later!

Importance of Data Interpretation

Understanding and interpreting data, especially through visualizations like histograms, is incredibly important in many fields. Whether you're in science, business, or even the humanities, the ability to analyze data and draw meaningful conclusions is a valuable skill. Histograms, in particular, help us see the distribution of data, identify patterns, and make informed decisions. By learning how to read and interpret histograms, you're not just answering questions on a test; you're developing a skill that will serve you well in many aspects of life. Data-driven decision-making is becoming increasingly prevalent, so the more comfortable you are with data analysis, the better equipped you'll be to succeed in a data-rich world. Remember, practice makes perfect! The more you work with histograms and other data visualizations, the easier it will become to extract valuable insights.

Conclusion

So, there you have it! We've successfully navigated through the histogram, figured out the number of students within a specific height range, and calculated the percentage of students within another range. Remember the key steps: understand the histogram, accurately read the bar heights, sum the relevant values, and apply the appropriate formulas. With a little practice, you'll become a pro at interpreting histograms and extracting valuable information from data. Keep practicing, stay curious, and you'll be well on your way to mastering data analysis! And remember, whether it's histograms or any other type of data, the goal is always to understand the story the data is telling us. Keep exploring and keep learning!