Question

For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4, 3, 5, 3, 7] please compute the following

1. measures of central tendency (3 points)

2. standard deviation ( 5 points)

3. is 18 an outlier? (5 points)

4. describe the shape of the distribution (2 points)

Answer 1

solution:

let X denote the given data set.

the below table shows the necessary computation with the given data

Measures of central tendency:

mean =

for median arranging the data in ascending order as follows:

median = (n+1)/2 = (15+1) / 2 = 8th item = 4

Mode : = maximum frequency value , which is 3 , so mode = 3

Q1 = middle of first half of data = (15+1)/4 = 4th item = 3

Q3 = middle of second half of data = (15+1)*3/4 = 12th item = 7

2)

standard deiviation :

3)

Interquartile range (IQR)= Q3-Q1 = 7-3 = 4

upper boundary for outlier = Q3+ 1.5(IQR) = 7 + (1.5*4) = 13

the observation 18 is greater than the upper boundary of 13 , so 18 is an outlier

4)

since mean = 5 is greater than the median = 4, so the distribution is positively skewed of skewed to the right.