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

Question

Arnold Odonnell · Accepted Answer

Step 1&amp;nbsp;If k is the number of classes and n is the number of observations, then for class intervals, select the smallest k such that&amp;nbsp;2k&amp;gt;n.&amp;nbsp;Here, n = 45. If k =5, then&amp;nbsp;2k=25=32&amp;nbsp;whichis less than n = 45. So, k = 5 not be put to use. If k = 6, then&amp;nbsp;2k—26=64&amp;nbsp;which is greater than n = 45. So, 6 classes should be used.&amp;nbsp;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&amp;nbsp;i≥H−Lk&amp;nbsp;Here, H=29 and L=0. I must then be chosen in a way thati≥H−Lk&amp;nbsp;⇒i≥29−06&amp;nbsp;⇒i≥4.833&amp;nbsp;Class width I is rounded up to 5 because 4.833 is nearly equal to 5.&amp;nbsp;Answer:&amp;nbsp;Class width = 5

user_27qwe · Accepted Answer

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 + \log_{2} (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 + \log_{2} (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 = \frac{Range}{Number of classes} = \frac{29}{Number of classes}

Substituting the value of the number of classes from the previous step, we get:

Class period = \frac{29}{1 + \log_{2} (45)}

By evaluating this expression, we can determine the appropriate class period for the given data set.

star233 · Accepted Answer

Result: 5Solution:Number&amp;nbsp;of&amp;nbsp;Classes=Range&amp;nbsp;of&amp;nbsp;DataClass&amp;nbsp;WidthHere, 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&#039;s assume the class width as x. Then the number of classes can be calculated as:29xTo 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&#039;s calculate the number of classes for different class sizes and evaluate their suitability:For x=5, the number of classes would be:295=5.8Since 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=2.9Again, this class size is not appropriate.For x=15, the number of classes would be:2915=1.93This class size is also not ideal.For x=20, the number of classes would be:2920=1.45Once 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&#039;s consider the range from 0 to 30 instead.For x=5, the number of classes would be:305=6This class size yields a whole number of classes, making it a suitable choice.

alenahelenash · Accepted Answer

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 + \log_{2} (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 + \log_{2} (45)

Calculating this expression:

k = 1 + \frac{\log (45)}{\log (2)}

Thus, the recommended class period size would be

⌈ k ⌉

to ensure a whole number of classes.

A set of data consists of 45 observations between 0

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