Question

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. class frequency f 52 - 55 9 72 - 76 1 σf = 24 data table lengths (in centimeters) of 24 adult fijian banded iguanas 52 68 70 55 65 61 70 67 68 62 54 71 58 61 74 63 62 58 62 59 63 66 62 61

Explanation:

Step1: Calculate class width

The minimum value is 52 and the maximum value is 74. We want 5 classes. Class - width $w=\frac{74 - 52}{5}=\frac{22}{5}= 4.4$. We round up to 5.

Step2: Define the classes

The first class is 52 - 56, the second is 57 - 61, the third is 62 - 66, the fourth is 67 - 71, and the fifth is 72 - 76.

Step3: Count frequencies

For the class 52 - 56: Count the number of data points in this range. There are 9.
For the class 57 - 61: Count the data points. There are 7.
For the class 62 - 66: Count the data points. There are 6.
For the class 67 - 71: Count the data points. There are 1.
For the class 72 - 76: Count the data points. There are 1.

Step4: Calculate relative frequencies

Total frequency $\sum f=9 + 7+6 + 1+1=24$.
Relative frequency of 52 - 56: $\frac{9}{24}=0.375$.
Relative frequency of 57 - 61: $\frac{7}{24}\approx0.292$.
Relative frequency of 62 - 66: $\frac{6}{24}=0.25$.
Relative frequency of 67 - 71: $\frac{1}{24}\approx0.042$.
Relative frequency of 72 - 76: $\frac{1}{24}\approx0.042$.

Answer:

The class 52 - 56 has the greatest relative frequency (0.375) and the classes 67 - 71 and 72 - 76 have the least relative frequency (approximately 0.042 each).