Mean, median, Mode, standard deviation and 10th and 90th percentiles

To find this value, multiply 30 by 0.9, giving you 27. This means that the 90th percentile is the 27th value in your data set. Repeat this process for the 10th percentile by multiplying 30 by 0.1, giving you 3. This means that the 10th percentile is the 3rd value in your data set. To compare the data using standard deviations, calculate the standard deviation for each data set and then compare the values. To superimpose smooth curves on the histograms, use a curve-fitting tool to find the best fit for the data and then plot it on the histogram. To identify skewness, look at the shape of the histogram and the values
  • #1
pinnacleprouk
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Homework Statement



I have two sets of data, each with 30 distances and 30 results, I have the mean, median, mode, range etc, I have drawn histograms and cumulative frequency curves, got the IRQ for both sets of data.

Now I need to compare the data using standard deviations and also find the 10th and 90th percentiles, could you explain the EASIEST way to do this without having to write a lot more things down, is there a formula or equation to get both these things.

Also how would I superimpose smooth curves to represent data distributions on the histograms and mark on the means, what data would I use and how would I identify skewness if any.

I just want descriptions on the easiest way to achieve this, I have not provided any numbers/data as i don't want you to do my work for me, rather just to give me the method in which I can do it myself.


Any help is greatly appreciated.

Thanks
 
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  • #2
To find the 10th and 90th percentile, use the definition. The score at the 90th percentile means it is higher than 90% of the data; in your case higher than 27 of the data points.
 

1. What is the difference between mean, median, and mode?

The mean, median, and mode are all measures of central tendency that describe the typical or average value of a dataset. The mean is calculated by taking the sum of all the data points and dividing by the total number of data points. The median is the middle value when the dataset is arranged in ascending or descending order. The mode is the most frequently occurring value in the dataset.

2. How is standard deviation calculated?

Standard deviation is a measure of how spread out the data points are from the mean. It is calculated by finding the difference between each data point and the mean, squaring those differences, taking the sum of the squared differences, dividing by the total number of data points, and then taking the square root of that value.

3. What do the 10th and 90th percentiles represent?

The 10th and 90th percentiles represent the values that divide the dataset into 10 equal parts and 90 equal parts, respectively. In other words, 10% of the data points fall below the 10th percentile, and 90% of the data points fall below the 90th percentile.

4. How are the 10th and 90th percentiles useful in data analysis?

The 10th and 90th percentiles can be used to understand the spread of the data and identify any outliers. For example, if the 10th and 90th percentiles are close together, it indicates that the data is tightly clustered around the mean. If there is a large difference between the 10th and 90th percentiles, it may suggest that there are extreme values in the dataset.

5. What is the significance of "mean ± standard deviation" in data interpretation?

"Mean ± standard deviation" is a commonly used notation to represent the range within which the majority of the data points fall. It indicates that the mean value is likely to be within one standard deviation above or below the mean. This helps to understand the spread of the data and the likelihood of a data point falling within a certain range.

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