In a somewhat similar fashion you can estimate the standard deviation based on the box plot: the standard deviation is approximately equal to the range / 4. the standard deviation is approximately equal to 3/4 * IQR.
These differences are called the deviations from the mean for each point. When visualized on a dotplot, these differences are viewed as distances between each point and the mean. A negative difference indicates that the data point is to the left of the mean (shown in blue on the graph below).
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.
Thus, the formula for the SD of a 2-value box can be expressed as: the difference between the two values in the box times the square root of the product of the fraction of the box with the larger value times the fraction of the box with the smaller value.
The middle “box” represents the middle 50% of scores for the group. The range of scores from lower to upper quartile is referred to as the inter-quartile range. The middle 50% of scores fall within the inter-quartile range. Seventy-five percent of the scores fall below the upper quartile.
Standard deviation plots are typically used in conjunction with mean plots. The mean plot would be used to check for shifts in location while the standard deviation plot would be used to check for shifts in scale. there is a shift in variation; greatest variation is during the summer months.
Under general normality assumptions, 95% of the scores are within 2 standard deviations of the mean. For example, if the average score of a data set is 250 and the standard deviation is 35 it means that 95% of the scores in this data set fall between 180 and 320.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.
To find the mean of the data set from the dot plot, you still have the option of listing out the data points, adding them up, and dividing by the number of dots in the plot.
A small standard deviation means that the values are all closely grouped together and therefore more precise. A large standard deviation means the values are not very similar and therefore less precise.
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