Statistics and probability
Course: Statistics and probability > Unit 3Lesson 4: Variance and standard deviation of a population
- Measures of spread: range, variance & standard deviation
- Variance of a population
- Population standard deviation
- The idea of spread and standard deviation
- Calculating standard deviation step by step
- Standard deviation of a population
- Mean and standard deviation versus median and IQR
- Concept check: Standard deviation
- Statistics: Alternate variance formulas
The idea of spread and standard deviation
See how distributions that are more spread out have a greater standard deviation.
Introduction to standard deviation
Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
For example, the blue distribution on bottom has a greater standard deviation (SD) than the green distribution on top:
A double dot plot with the upper half modeling the S D equals one and fifty nine hundredths and the lower half models the S D equals 2 and seventy nine hundredths. S D equals one and fifty nine hundredths dots range from 2 to 8 with a vertical line at around 5. The 2 and seventy nine hundredths dots range from 0 to 10 with a vertical line at around 5 and 25 hundredths.
Interestingly, standard deviation cannot be negative. A standard deviation close to indicates that the data points tend to be close to the mean (shown by the dotted line). The further the data points are from the mean, the greater the standard deviation.
Try it yourself
Which of the data distributions shown below has the greater standard deviation?
A double dot plot with the upper half modeling Distribution A and the lower half models Distribution B. Distribution A dots range from 0 to 10 with a vertical line at around 5 and one half. Distribution B dots range from 4 to 9 with a vertical line at around 6 and one half.
Want to join the conversation?
- what made this so important for math(16 votes)
- Statistics is used for a lot of everyday things. While you may not personally calculate statistical values, statistics is important for business, sports, video games, politics, medicine, software, etc. No matter what field you go into, that field will use statistics in some way, shape, or form.(26 votes)
- Can be standard deviation be zero?
then what is its significance? can we say this is a statistical problem?(2 votes)
- It can be zero if all entries have the same value. This is unlikely but possible to get such small sample from discrete distribution. Nevertheless, if you get big sample where each entry has exact the same value this should lead to the idea there is something wrong with the data source.(20 votes)
- why do I need to know this(10 votes)
- got this answer from the user screenbones: Statistics is used for a lot of everyday things. While you may not personally calculate statistical values, statistics is important for business, sports, video games, politics, medicine, software, etc. No matter what field you go into, that field will use statistics in some way, shape, or form.(3 votes)
- Can anyone please explain the difference for
Population Standard Deviation Vs Sample Standard Deviation?(3 votes)
- Population Standard Deviation is used when you're taking ALL the data observed as a set.
Sample Standard Deviation is used when you're takin only a SUBSET of the data observed in a set.(11 votes)
- how was the standard deviation determined?(2 votes)
- For this exercise, you don't have to calculate the standard deviations. Just look at the graphs and visually compare the distributions. Which distribution seems to have a wider spread of data around the mean? That is, which distribution includes points that are further from the mean (represented by the dotted line)? That is the distribution with the higher standard deviation.
The next lesson has a step-by-step walk-through for calculating the standard deviation.(5 votes)
- What can we infer from the data if we say that the data has huge variation or the data is spread out from the mean or the data has high std.deviation? What difference will it make in inference as opposed to the std.deviation being close to 0.(2 votes)
- Hi Vrisha,
When the data has a high SD (e.g., SD = 25), it means that the individual data points are spread out quite a bit.
On the other hand, if the data set has a smaller SD (e.g., SD = 0.3), you can infer that the data points are closer to the mean.(2 votes)
- If Data Spread is high is good or bed ?(2 votes)
- Depends on the situation, and mean. For example, let's take a movie's score. Let's say Marvel says it is a 4.5/5 movie.You would want a low MAD. But, if the score is 1/5, you would want a high MAD, like 4.(1 vote)
- sir what if i have 2 columns one with wages one with numbers of works how can we calculate s.d ,variance coefficient, coefficient of skewness what are tips tel us they different question(2 votes)
- how do you even find the standard deviation. I am confused. is it like the mode or mean or something?(2 votes)
- There's a formula for it; check out the next thing in this topic.(1 vote)
- How do we find the the frequency in dispersion?(2 votes)