“When she told me I was average, she was just being mean..”
It answers the following questions:
- What is the value that best describes the data set?
- How much a data set speads from its average value?
- What is the smallest and largest number in a data set?
In other words, it consists of measures of central tendency, variability, skewness and kurtosis.
Measures of central tendency are used to find the single value that best describes about the entire distribution. There are three main measures of central tendency: Mean, Median and Mode.
Mean
|
Average value
|
Median
|
Middle value
|
Mode
|
Most frequent value
|
Measures of Variability refers to the spread or dispersion of scores. There are four main measures of variability: Range, Inter quartile range, Standard deviation and Variance.
Range
|
Difference between max and min in a distribution
|
Standard Deviation
|
Average distance of scores in a distribution from
their mean
|
Variance
|
Square of the standard deviation
|
Skewness
|
Degree to which scores in a distribution are
spread out.
|
Kurtosis
|
Flatness or peakness of the curve
|
Examples:
Example 1: Suppose you are asked to calculate the average asset value of top stock funds and check whether there is any variability in the assets of these stock funds. You would answer this question with a measure of central tendency and variability.
Example 2: Suppose you are asked to provide a figure that best describes the annual salary offered to students in ABC College you would answer this question with a measure of central tendency and variability.
Download the example file
Using Excel:
1. If you haven’t already installed the Analysis ToolPak , Click the Microsoft Office button, then click on the Excel Options , and then select Add-Ins , Click Go, check the Analysis ToolPak box, and click Ok. How to Install Analysis ToolPak
2. Select Data tab, then click on the Data Analysis option, then selects Descriptive Statistics from the list and Click Ok. [Data tab >> Data Analysis >> Descriptive Statistics]
3. In the Input Range we select the data, and then select Output Range where you want the output to be stored. If you don’t specify the output range it will throw output in the new worksheet.
4. Check Summary Statistics and Confidence Level for Mean options. By default the confidence level is 95%. You can change the level as per the hypothesis standard of study.
5. When you click Ok, you will see the result in the selected output range.
Interpretation:
The average value is 5.533. The middle value is 6 and the most frequent value is 8. Negative skewness indicates a left skewed data. Negative kurtosis indicates a flat distribution. The 95% confidence level indicates you can be 95% sure that the true percentage of the population lies between 5.275 (5.533 – 0.258) and 5.791 (5.533 + 0.258).
Using Excel Functions:
You can accomplish the same task using excel functions such as AVERAGE, MEDIAN.MODE, SUM, STDEV, KURT, MAX, MIN, CONFIDENCE. Download the workbook
Do You Know ?
When to use mean, median and mode?
Mean – When your data is not skewed i.e normally distributed. In other words, there are no extreme values present in the data set (Outliers).
Median – When your data is skewed or you are dealing with ordinal (ordered categories) data (e.g. likert scale 1. Strongly dislike 2. Dislike 3.Neutral 4. Like 5. Strongly like)
Mode - When dealing with nominal (unordered categories) data.
In real life, suppose a company is considering expanding into an area and is studying the size of containers that competitors are offering. They would be more interested in the mode because they want to know what size tends to sell most often.
Interpretation:
The average value is 5.533. The middle value is 6 and the most frequent value is 8. Negative skewness indicates a left skewed data. Negative kurtosis indicates a flat distribution. The 95% confidence level indicates you can be 95% sure that the true percentage of the population lies between 5.275 (5.533 – 0.258) and 5.791 (5.533 + 0.258).
Using Excel Functions:
You can accomplish the same task using excel functions such as AVERAGE, MEDIAN.MODE, SUM, STDEV, KURT, MAX, MIN, CONFIDENCE. Download the workbook
Do You Know ?
When to use mean, median and mode?
Mean – When your data is not skewed i.e normally distributed. In other words, there are no extreme values present in the data set (Outliers).
Median – When your data is skewed or you are dealing with ordinal (ordered categories) data (e.g. likert scale 1. Strongly dislike 2. Dislike 3.Neutral 4. Like 5. Strongly like)
Mode - When dealing with nominal (unordered categories) data.
In real life, suppose a company is considering expanding into an area and is studying the size of containers that competitors are offering. They would be more interested in the mode because they want to know what size tends to sell most often.
About Author:
Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. He has over 10 years of experience in data science. During his tenure, he has worked with global clients in various domains like Banking, Insurance, Private Equity, Telecom and Human Resource.
why count is changing on changing confidence level
ReplyDeleteCorrections:
ReplyDeleteKurtosis
Flatness or peakness of the curve
should be
Kurtosis
Measures of rare, extreme values the curve
And
Negative kurtosis indicates a flat distribution.
should be
Negative kurtosis indicates a distribution with less rare, extreme values than a normal distribution.
(Explanation: Kurtosis does not measure "peakedness" or "flatness." Those are historically incorrect descriptions.)