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How does a box plot show normal distribution?
The box plot shape will show if a statistical data set is normally distributed or skewed. When the median is in the middle of the box, and the whiskers are about the same on both sides of the box, then the distribution is symmetric.
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
Can you get standard deviation from box plot?
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.
How do you use the Empirical Rule in statistics?
An example of how to use the empirical rule
- Mean: μ = 100.
- Standard deviation: σ = 15.
- Empirical rule formula: μ – σ = 100 – 15 = 85. μ + σ = 100 + 15 = 115. 68% of people have an IQ between 85 and 115. μ – 2σ = 100 – 2*15 = 70. μ + 2σ = 100 + 2*15 = 130. 95% of people have an IQ between 70 and 130. μ – 3σ = 100 – 3*15 = 55.
Can you find the mean with a box plot?
A boxplot, also called a box and whisker plot, is a way to show the spread and centers of a data set. Measures of spread include the interquartile range and the mean of the data set. Measures of center include the mean or average and median (the middle of a data set). The minimum (the smallest number in the data set).
How do you solve an empirical rule problem?
Solving Empirical Rule Questions
- Draw out a normal curve with a line down the middle and three to either side.
- Write the values from your normal distribution at the bottom.
- Write the percents for each section (you will need to memorize them!)
- Determine the section of the curve the question is asking for and shade it in.
How do you describe a Boxplot shape?
A boxplot can show whether a data set is symmetric (roughly the same on each side when cut down the middle) or skewed (lopsided). If the longer part of the box is to the right (or above) the median, the data is said to be skewed right. If the longer part is to the left (or below) the median, the data is skewed left.