Question

Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 54 61 55 61 65 56 57 62 56 63 60 63 55 57 78 a. Find the quartiles. The first? quartile, Upper Q 1?, is ? The second? quartile, Upper Q 2?, is? The third? quartile, Upper Q 3?, is ? ?(Type integers or? decimals.) b. Find the interquartile range. The interquartile range? (IQR) is?

Answer 1

First the data has to be sorted in ascending order of magnitude.

Total data points = 15

15/4 = 3.75 th point in the sorted data will be Q₁

So, Q₁ = 56

15/2 = 7.5 th point in the sorted data will be Q₂

So, Q₂ = 60

15 *3/4 = 11.25 th point in the sorted data will be Q₃

So, Q₃ = 63

Interquarile range IQR= Q₃ - Q₁ = 63 - 56 = 7

c) To find the outlier,

Lower bound = Q₁ - 1.5IQR = 56 - (1.5*7) = 45.5

Upper bound = Q₃ + 1.5IQR = 63 + (1.5*7) = 73.5

There is one point 78 which is outside the upper bound, so that is an outlier.