If you have 66 data observations in a sample, how many classes (bins) does the sturges' rule recommend for you to construct a fr
1 answer:
According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7
Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.
Given,
n = 66
We know that,
According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:
Here, n is equal to 66 and by substituting the value to the equation we get:
k = 7.0444
k ≈ 7
Learn more about Sturge's rule here: brainly.com/question/28184369
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Answer:
a)
So we expected about 75% within two deviations from the mean
b)
So we expected about 55.6% within 1.5 deviations from the mean
And the limits are:
c) We can calculate how many deviations we are within the mean with the limits with this formula:
And using the lower limit we got:
And with the upper limit we got:
So then the value of k =4 and the percentage is given by:
Step-by-step explanation:
Previous concepts and Data given
reprsent the population mean
represent the population standard deviation
The Chebyshev's Theorem states that for any dataset
• We have at least 75% of all the data within two deviations from the mean.
• We have at least 88.9% of all the data within three deviations from the mean.
• We have at least 93.8% of all the data within four deviations from the mean.
Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:
Part a
For this case we can find the percentage required replaincg k =2 and we got:
So we expected about 75% within two deviations from the mean
Part b
For this case we can find the percentage required replaincg k =2 and we got:
So we expected about 55.6% within 1.5 deviations from the mean
And the limits are:
Part c
We can calculate how many deviations we are within the mean with the limits with this formula:
And using the lower limit we got:
And with the upper limit we got:
So then the value of k =4 and the percentage is given by: