Pregunta
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te bepaal hoeveel klasse om te gebruik indien jy 'n frekwensietabel van die data moet opstel. Consider the dataset below containing marks obtained by 20 students in a Mathematics test. Use Sturge's rule to determine h many classes to use if you have to construct a frequency table of the data. \( \begin{array}{llllllllllllllllll}11 & 12 & 13 & 14 & 15 & 15 & 16 & 16 & 17 & 18 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 26\end{array} 28 \) A. 6 B. 10 C. 7 D. 5 E. 4

Ask by Macdonald Clark. in South Africa
Mar 15,2025

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The number of classes to use is 5.

Solución

To determine the number of classes to use when constructing a frequency table of the data using Sturge's rule, we need to follow these steps: 1. Calculate the number of classes using Sturge's rule formula: \[ \text{Number of classes} = 1 + 3.3 \times \log_{10} (n) \] where \( n \) is the number of data points. 2. Round the calculated number of classes to the nearest whole number. Let's calculate the number of classes using Sturge's rule for the given dataset. Calculate the value by following steps: - step0: Calculate: \(1+3.3\log_{10}{\left(20\right)}\) - step1: Simplify: \(1+4.293399\) - step2: Calculate: \(5.293399\) The number of classes to use when constructing a frequency table of the data using Sturge's rule is approximately 5.29. Rounding this to the nearest whole number, we get 5 classes. Therefore, the correct answer is D. 5.

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Mind Expander

Sturge's Rule is a handy formula for determining the number of classes (k) needed for a frequency distribution, which is calculated as \( k = 1 + 3.322 \log_{10}(n) \), where n is the number of observations. In this case, you have 20 students, so applying the formula gives \( k \approx 1 + 3.322 \log_{10}(20) \). This simplifies to roughly 6. Hence, the answer is A. 6. Now, let’s put this into perspective! Historians often use similar formulas to analyze data trends across decades. By breaking down massive amounts of information into comprehensible segments, they can identify patterns and significant events, just like how you can segment test scores for better analysis! Also, when setting up your frequency table, always double-check your calculations! It's common to dive into the formula but trip over the logarithm or rounding—double-checking can save you from confusion and incorrect conclusions. Remember, a few minutes of review can make your work sparkle!

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