Question

This Quesuon: 1 pt Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 60 62 55 65 57 63 56 57 65 63 64 63 59 54 78 0 a. Find the quartiles. The first quartile, Qq, is The second quartile, Q2, is The third quartile, Q3, is . (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is . (Type an integer or a decimal.) c. Identify any outliers. Choose the correct answer below. A. There exists at least one outlier in the data set at (Use a comma to separate answers as needed.) OB. There are no outliers in the data set.

Answer 1

Theory:- Quartiles in statistics are values that divide our data set into 4 quarters. There are 3 quartile, i.e. 1st quartile, 2nd quartile, 3rd quartile. 1st quartile of a data set is that value of the data set below which 25% observation lies. 2nd quartile of a data set is that value of the data set below which 50% observation lies. 3rd quartile of a data set is that value of the data set below which 75% observation lies. 2nd quartile also know as median of the data set.

Inter Quartile Range:- ( 3rd quartile - 1st quartile ).

Outlier:- An outlier is defined as being any point of data that lies over ( 3rd quartile + 1.5 × IQR ) or below which ( 1st quartile - 1.5 × IQR ).

Step for computing Quartile:- i) Arrange all the observations in increasing order. ii) Find how many observations are there. iii) Then find quartile.

Calculation:- We arrange the data in increasing order as,

54, 55, 56, 57, 57, 59, 60, 62, 63, 63, 63, 64, 65, 65, 78. So total number of observations is 15.

a)

1st quartile = 15×25% = 3.75 = 4th observation (approx)

2nd quartile = 15×50% = 7.5 = 8th observation (approx)

3r quartile = 15×75% = 11.25 = 12th observation (approx)

We clearly see that from the ordered data set 4th observation is 57, 8th observation is 62 and 12th observation is 64.

Hence, 1st quartile = 57, 2nd quartile = 62 and 3rd quartile = 64.

b)

Now, Inter Quartile Range is given by the formula,

IQR = 3rd quartile - 1st quartile = 64 - 57 = 7.

c)

Checking of outlier:-

(3rd quartile + 1.5 × IQR) = ( 64 + 1.5×7 ) = 74.5

(1st quartile - 1.5 × IQR) = ( 57 - 1.5×7 ) = 46.5

Hence, by the definition of outlier any value in the data set over 74.5 and below 46.5 is called outlier.

And from the ordered data set we clearly see that, highest value of the data set is 78 which is over 74.5 so observation 78 is called outlier.

So the correct option is A. There exist at least one outlier in the data set at 78.