Question

Given a data set consisting of 33 unique whole number observations, its five-number summary is: [19,32,47,61,77] how many observations are strictly less than 32?

Answer 1

Given a data set consisting of 33 unique whole number observations, its five-number summary is: [19,32,47,61,77] how many observations are strictly less than 32?

Solution: The five number summary denotes:

Minimum = 19

First Quartile = 32

Median = 47

Third Quartile = 61

Maximum = 77

Since there are an odd number of observations (33) in the data set, the First Quartile (32) must be at the (33+1)/4 = 8.5th position, meaning there are 7 numbers less than 32.

Therefore, there are 7 observations that are strictly less than 32

Answer 2

There are $\boxed7$ observations that are strictly less than 32.

Further Explanation:

In the summary of five numbers the value are, $\left[ {{\text{Min, }}{{\text{Q}}_{\text{1}}}{\text{, M, }}{{\text{Q}}_{\text{3}}}{\text{, Max}}} \right]$

Here, Min is the minimum value, ${Q_1}$ is the first quartile, M is the median, ${{\text{Q}}_{\text{3}}}$ is the third quartile and Max is the maximum value.

Given:

The given summary of the data is $\left[ {19,32,47,61,77} \right].$

There are 33 unique whole numbers.

Explanation:

From the summary of the data is $\left[ {19,32,47,61,77} \right].$

Minimum value of the data is 19.

First quartile of the data is 32.

Median of the data is 47.

Third quartile of the data is 61.

Maximum value of the data is 77.

The formula for the first quartile can be expressed as follows,

${Q_1} = {\left( {\dfrac{n}{4} + \dfrac{1}{4}} \right)^{th}}{\text{ term}}$

Substitute 33 for n in above equation to obtain the first quartile.

$\begin{aligned}{Q_1}&= {\left( {\frac{{33}}{4} + \frac{1}{4}} \right)^{th}}{\text{ term}}\\{\text{ }}&={\left( {\frac{{34}}{4}} \right)^{th}}{\text{ term}}\\&= {8.5^{th}}{\text{ term}}\\\end{aligned}$

The first quartile is 32 and its position is 8.5. therefore, seven observations are strictly less than 32.

There are $\boxed7$ observations that are strictly less than 32.

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Percentiles

Keywords: Given data, 33 unique numbers, whole numbers, observation, five-number, summary, [19,32,47,61,77], strictly less than 32, mean, standard normal distribution, standard deviation, measure, probability, mean, repeating, indicated, normal distribution, percentile, percentage.