Given a data set consisting of 33 unique whole number observations, its five - number summary is [ 12,24,38,51,64] How many observations are less than 38?

Question

Stella Calderon · Accepted Answer

Explain:  According to the question, given a data set consisting of 33 unique whole number observations and its five - number summary is  [12,24,38,51,64]  As these are the five number summary;  Minimum value of this 33 number is:  Minimum=12  First quartile:  Q1=24  Second Quartile (median):  Q2=38  Third quartile:  Q3=51  and maximum value:  Max=64  Therefore the data set of 33 number is divided into four group and median represent the mid value observation and we have 33 ( odd number of observation).  (33−1)4=8  number of observation in each group  Therefore the data set of 33 number is divided into four group and median represent the mid value observation and we have 33 ( odd number of observation).  =2×8  =16  As Q2=38 is median and as per the rules we have two group less than the median and two group are in more than median.

nghodlokl · Accepted Answer

Detailed explanation.

xleb123 · Accepted Answer

Step 1: The five-number summary provides us with key values that describe the distribution of the data. In this case, the five-number summary is given as [12, 24, 38, 51, 64].To find the number of observations less than 38, we can analyze the provided information. We know that the minimum value in the data set is 12 and the maximum value is 64. The five-number summary divides the data set into four quartiles, with the second quartile being the median.Since 38 is part of the third quartile (Q3), which is the upper half of the data, we can infer that any value less than 38 belongs to the first three quartiles (Q1, Q2, and Q3). Therefore, we need to determine the number of observations up to Q3, excluding Q3 itself.Step 2: To find the number of observations less than 38, we can subtract the value of Q3 from the total number of observations in the data set. Since we know the five-number summary and the number of unique observations is 33, we can calculate the number of observations less than 38 as:Number&amp;nbsp;of&amp;nbsp;observations&amp;nbsp;less&amp;nbsp;than&amp;nbsp;38=Q3−Q1−1Number&amp;nbsp;of&amp;nbsp;observations&amp;nbsp;less&amp;nbsp;than&amp;nbsp;38=38−12−1Number&amp;nbsp;of&amp;nbsp;observations&amp;nbsp;less&amp;nbsp;than&amp;nbsp;38=25Therefore, there are 25 observations in the data set that are less than 38.

Jazz Frenia · Accepted Answer

To find the number of observations less than 38, we need to identify the position of 38 in the five-number summary. Since 38 is the third value in the summary, it represents the median (Q2).The median (Q2) divides the data set into two equal halves. The values before the median are less than the median, and the values after the median are greater than the median.Therefore, the number of observations less than 38 is equal to the number of observations before the median (Q2), which is 24.In mathematical notation, we can express this as:Number&amp;nbsp;of&amp;nbsp;observations&amp;nbsp;less&amp;nbsp;than&amp;nbsp;38=Q2&amp;nbsp;position−1Number&amp;nbsp;of&amp;nbsp;observations&amp;nbsp;less&amp;nbsp;than&amp;nbsp;38=3−1=2Hence, there are 2 observations in the given data set that are less than 38.

Given a data set consisting of 33 unique whole number

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