Question

what is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 162 (b) 16 (c) 12.75 (d) 12 ​

Answer 1

Answer:

What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, and 16?

y=12. The value of the first quartile is 12 since Q1(lower quartile) is divided at the number 12.

PREMISES

y=the value of the first quartile for the numbers (observations) 15,18,10,20,23,28,12,16

CALCULATIONS

y=the value of the first quartile for the numbers (observations) 15,18,10,20,23,28,12,16

(1) First, place the list of numbers in numerical order from lowest to highest

(2) Then divide the list into 4 equal sections

(3) The quartiles are at the divisions

y=10,12,15,16,18,20,23,28

(2) The four equal sections are:

10,12

15,16

18,20

23,28

(3) The quartiles are:

Q1(lower quartile)=12

Q2 (middle quartile)=16 (median)

Q3 (upper quartile)=20

y=

12

C.H.

Step-by-step explanation:

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Answer 2

Answer:

The first Quartile of the given set of data = 12.

Answer is option(d).

Step-by-step explanation:

Quartile:

• The value that splits a list of integers into quarters can be calculated with the help of the quartile formula.
• The information is separated into quartiles after being initially organized in ascending order.

• While quartiles divide data into four equal halves, the median divides it into two equal portions.
• We may determine the first, second, and third quartiles using the quartile formula.

Quartile formula:

• A set of observations can be divided into four equal halves using the quartile formula. Between the first term and the median is where the first quartile is located.
• Second quartile is the median.
• The third quartile is the midpoint between the median and the final term. They are denoted mathematically as follows:

• The quartiles are shown as, when the set of observations is organised in ascending order.
•      First Quartile (Q1) = ((n + 1)/4)thTerm
• Second Quartile (Q2) = (n + 1)/2)th term
• Third Quartile (Q3)  = (3(n + 1)/4)th Term

    Given observations are

       15, 18, 10, 20, 23, 28, 12

 To find the First Quartile/Lower Quartile.

 Arrange the given numbers in ascending order.

       10, 12, 15, 18, 20, 23, 28                                                        

               Here there are 7 numbers

             median is the  4th term = 18

           First Quartile(Q1) = (7+1)/4th term

                                        = 2nd term

                                        = 12

         Hence, the first quartile = 12

Know more about Quartiles:

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