High School

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

Find the mean and standard deviation of the 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

Answer :

The mean of the given data is 46.5 and the standard deviation is 4.89. These values are calculated using the given sum of data, the number of data points, and the sum of the squares of data. Option C.

The mean of a data set is found by taking the sum of the data and dividing it by the number of data points.

In this case, the sum of the data is given as Ex = 279 and the number of data points as n = 6.

Therefore, the mean is 279/6 = 46.5.

The standard deviation measures the amount of variation or dispersion in a data set.

This is calculated using the given Ex² = 13 093 and the previously found mean (46.5).

The formula for standard deviation is sqrt((Ex²/n) - (mean)²).

Plugging in our values gives us sqrt((13 093/6) - (46.5)²) = 4.89.

Therefore, the correct option is C. mean =46.5, standard deviation = 4.89.

Learn more about the topic of Statistics here:

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