Question

se the accompanying data set to complete the following actions.

a. Find the quartiles.

b. Find the interquartile range.

c. Identify any outliers.

59 65 60 57 64 64 65 65 54 64 59 65 64 60 7959  65  60  57  64  64  65  65  54  64  59  65  64  60  79

a. Find the quartiles.

The first​ quartile,

The second​ quartile,

The third​ quartile,

​(Type integers or​ decimals.)

Answer 1

First arrange the given dataset in increasing order

N = 30

So first divide the arrage data set into two eqaul parts each with 15 bservations.

The median of first part is our first quartile = 59

The median of whole arrage data set is nothing but the 2nd quartile

Since there are even number of values , so median ( 2nd quartile ) is the average of middel two values. That is average of (n/2)th value and {(n/2)+1}th value

= average of (30/2)th = 15th value and 16th value = (64+64)/2 = 64

So second quartile = 64

The median of first part is our first quartile = 65

Look the following image:

b. Find the interquartile range.

Formula of Inter Quartile Range (IQR) is as follows:

IQR = 3rd Quartile - 1st Quartile = 65 - 59 = 6

c) Consider the following two limits

Q₁ - (1.5 * IQR) = 59 - (1.5 *6) = 50

Q₃ + (1.5 * IQR) = 59 + (1.5 *6) = 68

So the values outsides ( 50, 68 ) are called Outliesrs.

So there are two outliers as 79 and 79