Question

The following data are the the weights of 25 students recorded as follows: 39, 43, 36, 38, 46, 51, 33, 44, 44, 43, 63, 23, 35, 39, 23, 24, 33, 36, 49, 21, 30, 32, 33, 35, 36

Find the Mean, Median, Q1, Q3, IQR, Outliers (If there are no outliers, write "None")

a) Without sketching the graph, reason and explain whether the distribution is symmetric or skewed.

(b) Draw a sketchplot of this data

Answer 1

Here,

Mean

Sorting the observations in ascending order of magnitude, we get

21,23,23,24,30,32,33,33,33,35,35,36,36,36,38,39,39,43,43,44,44,46,49,51,63

To find Q₁,

th observation in the sorted data set.

6^th observation in the sorted data set = 32

7^th observation in the sorted data set = 33

So,

To find Q₃,

th observation in the sorted data set.

19^th observation in the sorted data set = 43

20^th observation in the sorted data set = 44

So,

IQR = Q₃ - Q₁ = 43.5 - 32.5 = 11

lower bound for outlier = Q₁ - 1.5*IQR = 32.5 - (1.5*11) = 16

upper bound for outlier = Q₃ + 1.5*IQR = 43.5 + (1.5*11) = 60

There is one observation 63 which is outside the interval (16, 60), so it can be considered as outlier.

b)