Question

marla records the total rainfall, in centimeters, each month in april and may.

what statement is correct?
a. the mean and standard deviation of april are larger than those of may.
b. the mean and standard deviation of may are larger than those of april.
c. the mean of april is larger than the mean of may, but the standard deviation of april is smaller.
d. the mean of may is larger than the mean of april, but the standard deviation of may is smaller.
a
b
c
d

Explanation:

Step1: Calculate the mean of April

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). For April, \(n = 4\), \(x_1=6,x_2 = 4,x_3=8,x_4 = 12\). Then \(\bar{x}_{April}=\frac{6 + 4+8+12}{4}=\frac{30}{4}=7.5\)

Step2: Calculate the mean of May

For May, \(n = 4\), \(x_1=7,x_2 = 1,x_3=1,x_4 = 7\). Then \(\bar{x}_{May}=\frac{7 + 1+1+7}{4}=\frac{16}{4}=4\)

Step3: Calculate the standard deviation of April

The formula for the standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}\).
\((x_1-\bar{x}_{April})^{2}=(6 - 7.5)^{2}=(-1.5)^{2}=2.25\), \((x_2-\bar{x}_{April})^{2}=(4 - 7.5)^{2}=(-3.5)^{2}=12.25\), \((x_3-\bar{x}_{April})^{2}=(8 - 7.5)^{2}=(0.5)^{2}=0.25\), \((x_4-\bar{x}_{April})^{2}=(12 - 7.5)^{2}=(4.5)^{2}=20.25\)
\(\sum_{i = 1}^{4}(x_{i}-\bar{x}_{April})^{2}=2.25+12.25 + 0.25+20.25=35\)
\(s_{April}=\sqrt{\frac{35}{3}}\approx3.42\)

Step4: Calculate the standard deviation of May

\((x_1-\bar{x}_{May})^{2}=(7 - 4)^{2}=9\), \((x_2-\bar{x}_{May})^{2}=(1 - 4)^{2}=9\), \((x_3-\bar{x}_{May})^{2}=(1 - 4)^{2}=9\), \((x_4-\bar{x}_{May})^{2}=(7 - 4)^{2}=9\)
\(\sum_{i = 1}^{4}(x_{i}-\bar{x}_{May})^{2}=9+9 + 9+9=36\)
\(s_{May}=\sqrt{\frac{36}{3}} = 3.46\)

Answer:

C. The mean of April is larger than the mean of May, but the standard deviation of April is smaller