Question

weights of 67 college students in kilograms in september of freshman year are provided in the accompanying data set. construct a frequency distribution. begin with a lower class limit of 40.0 kg and use a class width of 10.0 kg. does the distribution appear to be a normal distribution? click the icon to view the freshman weights. weights weights 71.8 97.2 73.8 92.9 68.0 58.8 64.0 56.0 70.0 57.9 50.0 70.8 66.9 56.1 70.0 60.8 52.9 91.7 57.2 67.2 58.0 48.8 68.2 69.2 86.8 81.2 60.2 51.9 69.9 63.0 56.3 68.2 67.9 53.9 80.3 64.0 56.7 63.2 53.7 56.1 54.1 72.9 77.2 63.2 51.2 59.1 65.2 53.3 61.7 55.0 74.1 74.3 64.2 64.2 56.9 64.0 60.3 64.1 65.8 52.3 70.9 54.9 65.2 75.2 41.8 74.1 93.9

Explanation:

Step1: Determine the class intervals

The first class has a lower limit of \(40.0\) and class - width \(w = 10.0\).
The class intervals are:

• \(40.0 - 49.9\)
• \(50.0 - 59.9\)
• \(60.0 - 69.9\)
• \(70.0 - 79.9\)
• \(80.0 - 89.9\)
• \(90.0 - 99.9\)

Step2: Count the frequencies

• For the class \(40.0 - 49.9\):

Count the number of data points in this range. The data points \(41.8\) are in this class. So, the frequency \(f_1=1\)

• For the class \(50.0 - 59.9\):

Count the data points \(51.2,51.9,53.7,53.9,54.1,55.0,56.1,56.7,56.9,58.8,59.1\). So, the frequency \(f_2 = 11\)

• For the class \(60.0 - 69.9\):

Count the data points \(60.2,61.7,62.2,63.2,64.0,64.1,64.2,65.2,65.8,67.2,67.9,68.2,68.0\). So, the frequency \(f_3=13\)

• For the class \(70.0 - 79.9\):

Count the data points \(70.0,70.8,71.8,72.9,73.8,74.1,75.2\). So, the frequency \(f_4 = 7\)

• For the class \(80.0 - 89.9\):

Count the data points \(80.3,81.2\). So, the frequency \(f_5=2\)

• For the class \(90.0 - 99.9\):

Count the data points \(92.9,93.9,97.2\). So, the frequency \(f_6=3\)

Answer:

Weight (kg)	Frequency
\(50.0 - 59.9\)	\(11\)
\(60.0 - 69.9\)	\(13\)
\(70.0 - 79.9\)	\(7\)
\(80.0 - 89.9\)	\(2\)
\(90.0 - 99.9\)	\(3\)