Question

In the following census population density dataset, what are the first, second, and third quartiles? 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 Select the correct answer below: Q1: 1 Q2: 27.5 Q3: 9857 Q1: 55 Q2: 110 Q3: 295 Q1: 55.5 Q2: 110 Q3: 295 Q1: 25 Q2: 50 Q3: 75

Answer 1

Answer:

(C) Q1: 55.5 Q2: 110 Q3: 295

Step-by-step explanation:

Given the dataset:

$1,19,35,43,49,55,56,56,63,67,\\94,105,110,168,175,181,212,231,239,351,\\461,595,738,839,9857$

There are 25 items in the dataset.

To find Q2, We divide it into two equal parts and consider the middle term

$1,19,35,43,49,55,56,56,63,67,94,105,\\110\\168,175,181,212,231,239,351,461,595,738,839,9857$

Therefore: Q2 =110

Q1 = the median of the lower half of the data set.

Q3 = is the median of the upper half of the data set.

In the lower half of the data

$1,19,35,43,49,55,56,56,63,67,94,105$

Since there are even number of terms,

Median = (55+56)/2=55.5

Therefore: Q1=55.5

In the upper half of the data

$168,175,181,212,231,239,351,461,595,738,839,9857$

Since there are even number of terms,

Median = (239+351)/2=295

Therefore: Q3=295

Q1: 55.5,  Q2: 110,  Q3: 295

The correct option is C.

Answer 2

The first, second and third quartiles of the given data set are;

Q1 = 55.5

Q2 = 110

Q3 = 295

The given dataset showing population density is;

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.

There are 25 numbers in this dataset.

The dataset is already arranged from least to greatest and as such let us write the first 12 terms in that order and the last 12 terms and let the middle term be sandwiched between both set of 12;

First twelve terms; 1, 19, 35, 43, 49, 55, 56, 56, 63, 67, 94, 105

Middle Term; 110

Last twelve terms; 168, 175, 181, 212, 231, 239, 351, 461, 595, 738, 839, 9857

A) The first quartile is the median of the First twelve terms. Since there are even digits, then;

Median = (sum of two middle terms)/2

Median = (55 + 56)/2

Median = 55.5

Thus;

First Quartile; Q1 = 55.5

B) Second quartile is the median of the original set of 25 numbers and it is 110.

Thus;

Second quartile; Q2 = 110

C)  The third quartile is the median of the last twelve terms. Since there are even number of digits, then;

Median = (239 + 351)/2

Median = 295

Thus;

Third Quartile; Q3 = 295

Read more about first and third quartiles at; https://brainly.com/question/3514929