A frequency table is given as follows: (1, 5), (2, 6), (3, 8), (4, 3), (5, 2). The first element in each pair represents a value, and the second element represents the frequency of that value. What is the variance of the frequency table?
Answer
Step 2: Calculate the variance (\(\sigma^2\)) of the dataset. The variance is calculated as \(\sigma^2 = \frac{\sum f*(x-\mu)^2}{N}\), where \(f\) is the frequency of each value \(x\), \(\mu\) is the mean, and \(N\) is the total frequency. In this case, \(\sigma^2 = \frac{5*(1-2.42)^2 + 6*(2-2.42)^2 + 8*(3-2.42)^2 + 3*(4-2.42)^2 + 2*(5-2.42)^2}{24} = 1.61\).
Step 1 ：Step 1: Calculate the mean (\(\mu\)) of the dataset. The mean is calculated as \(\mu = \frac{\sum f*x}{N}\), where \(f\) is the frequency of each value \(x\), and \(N\) is the total frequency. In this case, \(\mu = \frac{1*5 + 2*6 + 3*8 + 4*3 + 5*2}{5+6+8+3+2} = \frac{58}{24} = 2.42\).
Step 2 ：Step 2: Calculate the variance (\(\sigma^2\)) of the dataset. The variance is calculated as \(\sigma^2 = \frac{\sum f*(x-\mu)^2}{N}\), where \(f\) is the frequency of each value \(x\), \(\mu\) is the mean, and \(N\) is the total frequency. In this case, \(\sigma^2 = \frac{5*(1-2.42)^2 + 6*(2-2.42)^2 + 8*(3-2.42)^2 + 3*(4-2.42)^2 + 2*(5-2.42)^2}{24} = 1.61\).
