Use the following information to answer Question 7 and Question 8.

The marks of six students in a Mathematics test are represented by the variable [tex]x[/tex]. The following data was produced: [tex]n = 6[/tex], [tex]\Sigma x = 279[/tex], and [tex]\Sigma x^2 = 13,093[/tex].

Find the mean and standard deviation of the following data.

A. mean = 46.5, standard deviation = 5.82
B. mean = 52.5, standard deviation = 4.89
C. mean = 46.5, standard deviation = 4.89
D. mean = 52.5, standard deviation = 5.82

Given the data, we can use the formulas for calculating the mean and standard deviation of a dataset. The mean (average) is calculated using the formula:

Mean (μ) = Σx / n

where Σx is the sum of all the individual data points, and n is the total number of data points. Substituting the given values, we have:

Mean (μ) = 279 / 6 = 46.5

Next, the standard deviation (σ) is calculated using the formula:

Standard Deviation (σ) = √(Σx2 / n - μ2)

where Σx2 is the sum of the squares of all the data points, n is the total number of data points, and μ is the mean. Substituting the given values, we have:

Standard Deviation (σ) = √(13093 / 6 - 46.5²) ≈ 4.89

Hence, the correct answer is C, with a mean of 46.5 and a standard deviation of approximately 4.89. This implies that the average marks of the students are around 46.5, and the individual marks tend to vary from this average by about 4.89 marks.

Understanding how to calculate the mean and standard deviation is essential in descriptive statistics. These measures provide insights into the central tendency and spread of a dataset. Standard deviation quantifies the amount of variability or dispersion in a set of values, helping to assess the reliability of the mean as a representative value.

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