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Video Transcript
Let us first have a look on the table. So in party sample. Mhm has the largest gender division because it is most bell shaped and simple and sample B. And smallest standard division as it has lowest typical distance from me. Now let us have explanation for this standard division. Major of how for it observed value is from mean. And belts of the distribution is symmetric about means from graph which he did values me are from. And in leashed bell shaped distribution like implored be values are close to mean and it has smaller standard division compared to the belch of this distribution. Soft in he is correct for party. Now coming to the part B. In part B. Temple C. Because it is not Meltem This is the right answer. Let's have the explanation. The empirical rule doesn't apply to all data sets. It a place only to those that are Bell said so in this option and is correct. This is the answer. Hope you understand the question. Thank you.
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Video Transcript
right. You need to look at these three graphs and you have to quickly interpret the standard deviation of the graph. So part A is asking you which set has the greatest sample standard deviation. So the first graph kind of resembles this, we've got our tallest tower in the center and then it's very symmetric as we go in each direction. And the short tower represents 456789 and 10. Now your next graph spans the same amount, but we've got tall towers at four, then we have a shorter tower at five and we've got no towers at 67 and eight and then at nine again we're symmetric. And then we've got our tall tower here and then your final graph has nothing at four and five the most is at seven. And on each side were symmetric, so we have nothing at four five, this is 678 and then we have nine and 10. So keep in mind what standard deviation is? Standard deviation is going to be the spread of the data and we have a higher standard deviation as we have more data away from the center. So think about where the center is for each of these grass. The center is here for this graph, the center is here for this graph and the center is here for this graph. So in this graph here we have most of the data huddled around the center, so because most of the data is huddled around the center, this has the lowest standard deviation and which one has the most data farthest away from the standard deviation, or farthest away from the mean, or the center right here has most of the data very far away from that center. So this one here has the largest standard deviation. So therefore for part A it says determine which data set has the greatest sample standard deviation. So for part A you're going to set that say that data set to has the greatest standard deviation and which one has the least sample standard deviation. You could say that data set three has the least standard deviation. Now, for part B, it is asking you how are the data sets? The same? So the data sets are the same because in each case the center is at seven. So therefore, you could say they're medians are all equal to seven and they're mean, we'll all be seven. Now, how are they different? They're going to be different because of their mode. The mode in the first graph is seven because that's where the tallest tower is, the mode. In the third graf is seven because that's where the tallest tower is. But in data set to the mode is at 10 and at four. So therefore they're different by way of their modes. Their range is also different because range is highest minus lowest, so the highest minus the lowest here would be 10 minus four or six. The highest minus the lowest in this next one would also be 10 minus six. Yeah, or sorry 10 minus four which is six, but in this case our highest minus lowest is only eight minus six. Highest is 86 So the ranges are different as well. So hopefully that helped you again, the more sets more pieces of data further from the center or from the mean, the higher the standard deviation.
A visual interpretation of numerical data showing the number of data points falling within a specified range of values
What is a Histogram?
A histogram[1] is used to summarize discrete or continuous data. In other words, it provides a visual interpretation of numerical data by showing the number of data points that fall within a specified range of values (called “bins”). It is similar to a vertical bar graph. However, a histogram, unlike a vertical bar graph, shows no gaps between the bars.
Parts of a Histogram
- The title: The title describes the information included in the histogram.
- X-axis: The X-axis are intervals that show the scale of values which the measurements fall under.
- Y-axis: The Y-axis shows the number of times that the values occurred within the intervals set by the X-axis.
- The bars: The height of the bar shows the number of times that the values occurred within the interval, while the width of the bar shows the interval that is covered. For a histogram with equal bins, the width should be the same across all bars.
Importance of a Histogram
Creating a histogram provides a visual representation of data distribution. Histograms can display a large amount of data and the frequency of the data values. The median and distribution of the data can be determined by a histogram. In addition, it can show any outliers or gaps in the data.
Distributions of a Histogram
A normal distribution: In a normal distribution, points on one side of the average are as likely to occur as on the other side of the average.
A bimodal distribution: In a bimodal distribution, there are two peaks. In a bimodal distribution, the data should be separated and analyzed as separate normal distributions.
A right-skewed distribution: A right-skewed distribution is also called a positively skewed distribution. In a right-skewed distribution, a large number of data values occur on the left side with a fewer number of data values on the right side. A right-skewed distribution usually occurs when the data has a range boundary on the left-hand side of the histogram. For example, a boundary of 0.
A left-skewed distribution: A left-skewed distribution is also called a negatively skewed distribution. In a left-skewed distribution, a large number of data values occur on the right side with a fewer number of data values on the left side. A right-skewed distribution usually occurs when the data has a range boundary on the right-hand side of the histogram. For example, a boundary such as 100.
A random distribution: A random distribution lacks an apparent pattern and has several peaks. In a random distribution histogram, it can be the case that different data properties were combined. Therefore, the data should be separated and analyzed separately.
Example of a Histogram
Jeff is the branch manager at a local bank. Recently, Jeff’s been receiving customer feedback saying that the wait times for a client to be served by a customer service representative are too long. Jeff decides to observe and write down the time spent by each customer on waiting. Here are his findings from observing and writing down the wait times spent by 20 customers:
The corresponding histogram with 5-second bins (5-second intervals) would look as follows:
We can see that:
- There are 3 customers waiting between 1 and 35 seconds
- There are 5 customers waiting between 1 and 40 seconds
- There are 5 customers waiting between 1 and 45 seconds
- There are 5 customers waiting between 1 and 50 seconds
- There are 2 customers waiting between 1 and 55 seconds
Jeff can conclude that the majority of customers wait between 35.1 and 50 seconds.
How to Create a Histogram
Let us create our own histogram. Download the corresponding Excel template file for this example.
Step 1: Open the Data Analysis box. This can be found under the Data tab as Data Analysis:
Step 2: Select Histogram:
Step 3: Enter the relevant input range and bin range. In this example, the ranges should be:
- Input Range: $C$10:$D$19
- Bin Range: $F$9:$F$24
Make sure that “Chart Output” is checked and click “OK”.
Download the Template Example to make one on your own!
Related Readings
Thank you for reading CFI’s guide on Histogram. To keep learning and advancing your career, the following resources will be helpful:
- Types of Graphs in Excel
- Dashboard Creation in Excel
- Excel Shortcuts PC & Mac
- List of Excel Functions
Article Sources
- Histogram