Answer to Question #89701 in Statistics and Probability for Surya

Question

Table 1
3.80 3.77 3.70 3.74 3.70
3.86 3.76 3.68 3.67 3.57
3.83 3.70 3.80 3.74 3.67
3.78 3.74 3.73 3.65 3.66
3.75 3.64 3.78 3.73 3.64

Based on Table 1,

a). Calculate the mode and mean,
b). Calculate the median and standard deviation

Answer 1

In increasing order: 3.57, 3.64, 3.64, 3.65, 3.66, 3.67, 3.67, 3.68, 3.7, 3.7, 3.7, 3.73, 3.73, 3.74, 3.74, 3.74, 3.75, 3.76, 3.77, 3.78, 3.78, 3.8, 3.8, 3.83, 3.86

The mode is the most often value: here these are 3.70 (3 times) and 3.74 (3 times).

The mean is the sum of all the values (93.09) divided by the number of values (25): 3.72

The median is the value in the middle of the set in increasing order; the 13th value is 3.73

The standard deviation is defined by

$$\sigma = \sqrt{\frac{\sum_i (x_i - \langle x \rangle)^2}{N-1}}$$

with already calculated <x> = 3.72 and N = 25, thus the standard deviation is 0.07