How do we calculate the range of values that fall within standard deviations?

Frequently Asked Questions Python FAQ
1

Question

In the context of this exercise, how do we calculate the range of values that fall within certain numbers of standard deviations?

Answer

To determine the range of values, we first need the value of a single standard deviation for a dataset. With this value, it is easy to then calculate the ranges of values.

# Given: 
# std_dev = standard deviation of the dataset
# mean = mean of the dataset

# 68% of the data falls between +/- 1 standard deviation
one_std_range = [mean - std_dev, mean + std_dev]

# 95% of the data falls between +/- 2 standard deviations
two_std_range = [mean - (2*std_dev), mean + (2*std_dev)]

# 99.7% of the data falls between +/- 3 standard deviations
three_std_range = [mean - (3*std_dev), mean + (3*std_dev)]
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2

Hi,

The answer of exercise 4, Topic 10 ( Standard Deviations and Normal Distribution, Part II) is 1360.

Has anyone reached this answer? And how?

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3

it’s always 68% of numbers of values

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4

one_std = 2000 * 0.68

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5

How can we determine whether it is 68%, 95%, or 99.7%?

if it is only +/-1 ; +/-2 is too vague. Since +/-10 or +/-100 falls into 68% distrution type, does +/-20 or +/-200 fall into 95% distrubtion type? If so, how about +/- 50 so something other example than +/-30?

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6

Not if we see it as standard deviations, not counting the outside edges, there are only three in either direction of the normal.

-1    |    1
 -----------
     68%

-2    |    2
 -----------
     95%

-3    |    3
 -----------
    99.7%

Keep in mind that the percentages represent area under the curve between the two Z-scores.

Z-score

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7

Thank you for your answers!

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9

lower_bound + upper_bound * 0.68

10

Just calculate 68% of 2000, and you can do like 0.68 * 2000 in the variable itself.

11

Everything great, but I really didn’t get what actually is one, two, three standard deviation. A dataset is suppose to have only one standard deviation only, I really didn’t understand it properly the concept.

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@joysasha standard deviation is a measurement of spread for a data. You can think of it as distance from the mean. There are no rules that says that a dataset can only have one standard deviation. Higher the standard deviation, the further the data spreads away from its mean value.

Standard deviation is different from variance because it has been scaled to the mean value, so that it can be comparable between two sets of data even if they are not measured on the same scale (for example, a data measured in the millions will have much higher variance and mean than one that’s measured in tens, but looking at the standard deviation can get rid of the scale and focus on the spread of the data). For a given data point, you can calculate how many standard deviations it is away from the mean. In a normal distribution this allows you to figure out if the data point is an outlier.

Hope this helps!