A set of data consists of 45 observations between 0

Isa Trevino

Isa Trevino

Answered question

2021-09-17

A set of data consists of 45 observations between 0 and 29. Which size would you advise for the class period?

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2021-09-18Added 109 answers

Step 1 
If k is the number of classes and n is the number of observations, then for class intervals, select the smallest k such that 2k>n
Here, n = 45. If k =5, then 2k=25=32 whichis less than n = 45. So, k = 5 not be put to use. If k = 6, then 2k26=64 which is greater than n = 45. So, 6 classes should be used. 
If H is the highest observed value and L is the lowest observed value, then for the class interval or class width i, select i such that 
iHLk 
Here, H=29 and L=0. I must then be chosen in a way that
iHLk 
i2906 
i4.833 
Class width I is rounded up to 5 because 4.833 is nearly equal to 5. 
Answer: 
Class width = 5

user_27qwe

user_27qwe

Skilled2023-06-12Added 375 answers

The class period refers to the width of each interval in the data set. To find an appropriate class period, we can use Sturges' formula, which is commonly used for determining the number of classes in a histogram.
Sturges' formula is given by:
Number of classes=1+log2(N) where N represents the number of observations in the data set.
In this case, the number of observations is 45, so substituting this value into the formula, we get:
Number of classes=1+log2(45)
Now, to find the class period, we can divide the range of values by the number of classes. The range of values is given as 0 to 29, so the range is 29.
Class period=RangeNumber of classes=29Number of classes
Substituting the value of the number of classes from the previous step, we get:
Class period=291+log2(45)
By evaluating this expression, we can determine the appropriate class period for the given data set.
star233

star233

Skilled2023-06-12Added 403 answers

Result: 5
Solution:
Number of Classes=Range of DataClass Width
Here, the range of the data is the difference between the maximum value and the minimum value, which in this case is 29 - 0 = 29.
Let's assume the class width as x. Then the number of classes can be calculated as:
29x
To determine the ideal class size, we need to consider a few factors such as the number of observations and the desired level of granularity in the data. If we have too few classes, the data may appear oversimplified, while too many classes may result in excessive detail.
To strike a balance, a common rule of thumb is to aim for around 5-20 classes. With 45 observations, we can select a value within this range to ensure a suitable level of granularity.
Let's calculate the number of classes for different class sizes and evaluate their suitability:
For x=5, the number of classes would be:
295=5.8
Since the number of classes should be a whole number, this class size is not suitable.
For x=10, the number of classes would be:
2910=2.9
Again, this class size is not appropriate.
For x=15, the number of classes would be:
2915=1.93
This class size is also not ideal.
For x=20, the number of classes would be:
2920=1.45
Once again, this class size is not suitable.
Based on these calculations, it appears that selecting a class size between 5 and 20 does not yield a whole number of classes. In such cases, it is advisable to adjust the range or consider using a different method for determining the class width.
However, if we expand the range slightly, we can find a suitable class size. Let's consider the range from 0 to 30 instead.
For x=5, the number of classes would be:
305=6
This class size yields a whole number of classes, making it a suitable choice.
alenahelenash

alenahelenash

Expert2023-06-12Added 556 answers

To determine the appropriate class period size for a set of data consisting of 45 observations between 0 and 29, we can use Sturges' formula. This formula provides an estimate for the number of classes (k) based on the number of observations (n) in the data set:
k=1+log2(n) where k represents the number of classes and n is the number of observations.
In this case, n=45. We can substitute this value into the formula:
k=1+log2(45)
Calculating this expression:
k=1+log(45)log(2)
Thus, the recommended class period size would be k to ensure a whole number of classes.

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