QuestionFind the 1st, 2nd, and 3rd quartiles of the population density data: $1,19,35,43,49,55,56,56,63,67,94,105,110,168,175,181,212,231,239,351,461,595,738,839,9857$ .

Studdy Solution

STEP 1

Assumptions1. The data set is already sorted in ascending order. . We are looking for the first, second, and third quartiles of the data set.

STEP 2

First, we need to understand what quartiles are. 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 Q, respectively.

STEP 3

To find the first quartile (Q1), we need to find the median of the first half of the data set. If the number of data points is odd, we do not include the middle value.

STEP 4

Our data set has25 values, so the first half of the data set includes the first12 values.
$1,19,35,43,49,55,56,56,63,67,94,105,110$

STEP 5

To find the median of these12 values, we take the average of theth and7th values.
$Q1 = (55 +56) /2$

STEP 6

Calculate the first quartile (Q1).
$Q1 = (55 +56) /2 =55.5$

STEP 7

To find the second quartile (Q2), which is also the median of the entire data set, we find the average of the13th and14th values.
$Q2 = (168 +175) /2$

STEP 8

Calculate the second quartile (Q2).
$Q2 = (168 +175) /2 =171.5$

STEP 9

To find the third quartile (Q3), we need to find the median of the second half of the data set. If the number of data points is odd, we do not include the middle value.

STEP 10

The second half of the data set includes the last12 values.
$168,175,181,212,231,239,351,461,595,738,839,9857$

STEP 11

To find the median of these values, we take the average of the6th and7th values.
$Q3 = (239 +351) /$

STEP 12

Calculate the third quartile (Q).
$Q = (239 +351) /2 =295$ The first quartile (Q) is55.5, the second quartile (Q2) is171.5, and the third quartile (Q) is295.

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QuestionFind the 1st, 2nd, and 3rd quartiles of the population density data: $1,19,35,43,49,55,56,56,63,67,94,105,110,168,175,181,212,231,239,351,461,595,738,839,9857$ .

Studdy Solution

STEP 1

Assumptions1. The data set is already sorted in ascending order. . We are looking for the first, second, and third quartiles of the data set.

STEP 2

First, we need to understand what quartiles are. 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 Q, respectively.

STEP 3

To find the first quartile (Q1), we need to find the median of the first half of the data set. If the number of data points is odd, we do not include the middle value.

STEP 4

Our data set has25 values, so the first half of the data set includes the first12 values.
$1,19,35,43,49,55,56,56,63,67,94,105,110$

STEP 5

To find the median of these12 values, we take the average of theth and7th values.
$Q1 = (55 +56) /2$

STEP 6

Calculate the first quartile (Q1).
$Q1 = (55 +56) /2 =55.5$

STEP 7

To find the second quartile (Q2), which is also the median of the entire data set, we find the average of the13th and14th values.
$Q2 = (168 +175) /2$

STEP 8

Calculate the second quartile (Q2).
$Q2 = (168 +175) /2 =171.5$

STEP 9

To find the third quartile (Q3), we need to find the median of the second half of the data set. If the number of data points is odd, we do not include the middle value.

STEP 10

The second half of the data set includes the last12 values.
$168,175,181,212,231,239,351,461,595,738,839,9857$

STEP 11

To find the median of these values, we take the average of the6th and7th values.
$Q3 = (239 +351) /$

STEP 12

Calculate the third quartile (Q).
$Q = (239 +351) /2 =295$ The first quartile (Q) is55.5, the second quartile (Q2) is171.5, and the third quartile (Q) is295.

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Studdy Solution

STEP 1

Assumptions1. The data set is already sorted in ascending order. . We are looking for the first, second, and third quartiles of the data set.

STEP 2

First, we need to understand what quartiles are. 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 Q, respectively.

STEP 3

To find the first quartile (Q1), we need to find the median of the first half of the data set. If the number of data points is odd, we do not include the middle value.

STEP 4

Our data set has25 values, so the first half of the data set includes the first12 values.1,19,35,43,49,55,56,56,63,67,94,105,1101,19,35,43,49,55,56,56,63,67,94,105,1101,19,35,43,49,55,56,56,63,67,94,105,110

STEP 5

To find the median of these12 values, we take the average of theth and7th values.Q1=(55+56)/2Q1 = (55 +56) /2Q1=(55+56)/2

STEP 6

Calculate the first quartile (Q1).Q1=(55+56)/2=55.5Q1 = (55 +56) /2 =55.5Q1=(55+56)/2=55.5

STEP 7

To find the second quartile (Q2), which is also the median of the entire data set, we find the average of the13th and14th values.Q2=(168+175)/2Q2 = (168 +175) /2Q2=(168+175)/2

STEP 8

Calculate the second quartile (Q2).Q2=(168+175)/2=171.5Q2 = (168 +175) /2 =171.5Q2=(168+175)/2=171.5

STEP 9

To find the third quartile (Q3), we need to find the median of the second half of the data set. If the number of data points is odd, we do not include the middle value.

STEP 10

The second half of the data set includes the last12 values.168,175,181,212,231,239,351,461,595,738,839,9857168,175,181,212,231,239,351,461,595,738,839,9857168,175,181,212,231,239,351,461,595,738,839,9857

STEP 11

To find the median of these values, we take the average of the6th and7th values.Q3=(239+351)/Q3 = (239 +351) /Q3=(239+351)/

STEP 12

Calculate the third quartile (Q).Q=(239+351)/2=295Q = (239 +351) /2 =295Q=(239+351)/2=295The first quartile (Q) is55.5, the second quartile (Q2) is171.5, and the third quartile (Q) is295.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Our data set has25 values, so the first half of the data set includes the first12 values.
$1,19,35,43,49,55,56,56,63,67,94,105,110$

To find the median of these12 values, we take the average of theth and7th values.
$Q1 = (55 +56) /2$

Calculate the first quartile (Q1).
$Q1 = (55 +56) /2 =55.5$

To find the second quartile (Q2), which is also the median of the entire data set, we find the average of the13th and14th values.
$Q2 = (168 +175) /2$

Calculate the second quartile (Q2).
$Q2 = (168 +175) /2 =171.5$

The second half of the data set includes the last12 values.
$168,175,181,212,231,239,351,461,595,738,839,9857$

To find the median of these values, we take the average of the6th and7th values.
$Q3 = (239 +351) /$

Calculate the third quartile (Q).
$Q = (239 +351) /2 =295$ The first quartile (Q) is55.5, the second quartile (Q2) is171.5, and the third quartile (Q) is295.