What is the frequency distribution of this data set: Character: Usage Rate: Bennett 87.30% Zhongli 82.40% Kazuha 79.80% Yelan 75.70% Raiden Shogun 73.30% Xingqiu 72.70% Xiangling 67.10% Hu Tao 64.80% Albedo 53.00% Yoimiya 48.90% Sangonomiya Kokomi 47.10% Arataki Itto 39.80% Kamisato Ayato 33.30% Yae Miko 31.80% Kamisato Ayaka 28.90% Sucrose 26.70% Venti 25.50% Shenhe 24.80% Xiao 21.30% Tartaglia 18.70% Ganyu 18.60% Diona 17.40% Fishcl 16.70% Gorou 16.50% Eula 14.50% Jean 14.30% Mona 13.80% Klee 13.20% Yunjin 10.00% Kujou Sara 7.90% Rosaria 7.70% Beidou 7.50% Diluc 3.80% Thoma 3.40% Ningguang 3.30% Yanfei 2.90% Noelle 2.60% Keqing 1.70% Qiqi 1.10% Barbara 1.10% Sayu 0.90% Chongyun 0.90% Kaeya 0.70% Lisa 0.60% Xinyan 0.40% Amber 0.40% Razor 0.20% Aloy 0.10%
Question
What is the frequency distribution of this data set: Character: Usage Rate: Bennett 87.30% Zhongli 82.40% Kazuha 79.80% Yelan 75.70% Raiden Shogun 73.30% Xingqiu 72.70% Xiangling 67.10% Hu Tao 64.80% Albedo 53.00% Yoimiya 48.90% Sangonomiya Kokomi 47.10% Arataki Itto 39.80% Kamisato Ayato 33.30% Yae Miko 31.80% Kamisato Ayaka 28.90% Sucrose 26.70% Venti 25.50% Shenhe 24.80% Xiao 21.30% Tartaglia 18.70% Ganyu 18.60% Diona 17.40% Fishcl 16.70% Gorou 16.50% Eula 14.50% Jean 14.30% Mona 13.80% Klee 13.20% Yunjin 10.00% Kujou Sara 7.90% Rosaria 7.70% Beidou 7.50% Diluc 3.80% Thoma 3.40% Ningguang 3.30% Yanfei 2.90% Noelle 2.60% Keqing 1.70% Qiqi 1.10% Barbara 1.10% Sayu 0.90% Chongyun 0.90% Kaeya 0.70% Lisa 0.60% Xinyan 0.40% Amber 0.40% Razor 0.20% Aloy 0.10%
Solution
The frequency distribution of a data set is a summary of the frequency of individual values or ranges of values in the data. Here's how you can create a frequency distribution for the given data set:
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First, you need to identify the range of the data. In this case, the usage rates range from 0.10% to 87.30%.
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Next, you need to decide on the number of classes or intervals for your frequency distribution. This can be arbitrary, but a common rule of thumb is to take the square root of the number of data points. In this case, there are 44 data points, so you might choose to have around 7 classes.
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Then, you need to calculate the width of each class. This is done by subtracting the lowest value from the highest value and dividing by the number of classes. In this case, (87.30 - 0.10) / 7 = 12.46, so each class might be 12.46% wide.
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Now, you can create a table with the classes in one column and the frequency in another. For each character, you would determine which class their usage rate falls into and increase the frequency for that class by one.
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Finally, you can calculate the relative frequency for each class by dividing the frequency by the total number of data points. This gives you the proportion of the data that falls into each class.
Here's an example of what the frequency distribution might look like:
| Class Interval | Frequency |
|---|---|
| 0.10 - 12.56 | 16 |
| 12.57 - 25.03 | 5 |
| 25.04 - 37.50 | 4 |
| 37.51 - 49.97 | 3 |
| 49.98 - 62.44 | 5 |
| 62.45 - 74.91 | 6 |
| 74.92 - 87.30 | 5 |
This is a simplified example and the actual frequency distribution might look slightly different depending on the exact class intervals you choose.
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