Answered

PLEASE HELP!!!!!



The data set represents the heights of players on a soccer team.


5.75, 5.16, 6, 5.25, 5.5, 6.25, 5.66, 5.33, 5.33, 6, 5.75. 5.66, 5.16


What is the interquartile range (IQR) of the data set?

A0.585
B1.09
C5.6
D5.875

Verified Answer :

Answer:

Option: A(0.585)

Step-by-step explanation:

After arranging our data in ascending order we get that:

5.16   5.16   5.25   5.33   5.33   5.5   5.66   5.66   5.75   5.75   6   6   6.25

Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.


  • \(Q_1\) is the "middle" value in the first half of the rank-ordered data set.

  • \(Q_2\) is the median value in the set.

  • \(Q_3\) is the "middle" value in the second half of the rank-ordered data set.

The interquartile range is equal to Q3-Q1.

So, the Median(\(Q_2\))of data is given by: 5.66

also the lower half is:

5.16   5.16   5.25   5.33   5.33   5.5

Hence, the middle value or median of this lower half of this data lie between 5.25 and 5.33 which is 5.29.

Hence, \(Q_1\)=5.29

Similarly the upper half is:

5.66   5.75   5.75   6   6   6.25

Hence, the middle value or median of this upper half of this data lie between 5.75 and 6 which is 5.875

Hence, \(Q_3\)=5.875

Hence, the interquartile range=\(Q_3-Q_1=5.875-5.29=0.585\)

Hence, option A is correct.


Related Questions