construct a frequency distribution and a relative frequency histogram for the data set using five classes…
construct a frequency distribution and a relative frequency histogram for the data set using five classes. which class has the greatest relative frequency and which has the least relative frequency? click the icon to view the data set. complete the table below. use the minimum data entry as the lower limit of the first class. data table lengths (in centimeters) of 24 adult fijan banded iguanas 52 64 70 55 64 60 70 54 68 61 54 71 50 60 74 61 61 57 62 58 61 65 62 60
Answer
Explanation:
Step1: Find range and class - width
First, find the minimum and maximum values in the data set. The minimum value is 52 and the maximum value is 87. The range $R = 87 - 52=35$. Since we want 5 classes, the class - width $w=\frac{35}{5}=7$.
Step2: Define class intervals
The first class has a lower limit of 52. The class intervals are: 52 - 58, 59 - 65, 66 - 72, 73 - 79, 80 - 86.
Step3: Calculate frequencies
Count the number of data points in each class:
- For the class 52 - 58, the frequency $f_1 = 3$ (the values 52, 54, 58).
- For the class 59 - 65, the frequency $f_2 = 9$ (the values 60, 60, 60, 61, 61, 61, 62, 62, 64).
- For the class 66 - 72, the frequency $f_3 = 6$ (the values 68, 70, 70, 71, 70, 68).
- For the class 73 - 79, the frequency $f_4 = 2$ (the values 74, 74).
- For the class 80 - 86, the frequency $f_5 = 4$ (the values 80, 81, 81, 85).
Step4: Calculate relative frequencies
The total number of data points $n = 24$. The relative frequency of a class is given by $rf=\frac{f}{n}$.
- For the class 52 - 58, $rf_1=\frac{3}{24}=0.125$.
- For the class 59 - 65, $rf_2=\frac{9}{24}=0.375$.
- For the class 66 - 72, $rf_3=\frac{6}{24}=0.25$.
- For the class 73 - 79, $rf_4=\frac{2}{24}\approx0.083$.
- For the class 80 - 86, $rf_5=\frac{4}{24}\approx0.167$.
The class with the greatest relative frequency is 59 - 65 and the class with the least relative frequency is 73 - 79.
Answer:
The class with the greatest relative frequency is 59 - 65 and the class with the least relative frequency is 73 - 79.