Math

QuestionFind the first, second, and third quartiles for the data set: 10,15,20,25,30,35,40,45,5010, 15, 20, 25, 30, 35, 40, 45, 50.

Studdy Solution

STEP 1

Assumptions1. The data set is 10,15,20,25,30,35,40,45,5010,15,20,25,30,35,40,45,50 . The data set is already ordered in ascending order3. The first quartile (Q1) is the median of the first half of the data4. The second quartile (Q) is the median of the whole data set5. The third quartile (Q3) is the median of the second half of the data

STEP 2

First, let's find the second quartile (Q2), which is the median of the whole data set. The median is the middle value when the data is ordered from least to greatest. If the data set has an odd number of observations, the median is the middle number. If the data set has an even number of observations, the median is the average of the two middle numbers.
In our case, the data set has9 observations, which is an odd number. So, the median is the middle number.
Q2=Median=5thnumber=30Q2 = Median =5th\, number =30

STEP 3

Now, let's find the first quartile (Q1). Q1 is the median of the first half of the data. Since the total number of observations is odd, we don't include the median (Q2) in either half. So, the first half of the data is 10,15,20,2510,15,20,25.
Again, this data set has an even number of observations, so the median is the average of the two middle numbers.
Q1=Medianoffirsthalf=Averageof2ndand3rdnumbers=(15+20)/2=17.5Q1 = Median\, of\, first\, half = Average\, of\,2nd\, and\,3rd\, numbers = (15+20)/2 =17.5

STEP 4

Finally, let's find the third quartile (Q3). Q3 is the median of the second half of the data. The second half of the data is 35,40,45,5035,40,45,50.
This data set also has an even number of observations, so the median is the average of the two middle numbers.
Q3=Medianofsecondhalf=Averageof2ndand3rdnumbers=(40+45)/2=42.Q3 = Median\, of\, second\, half = Average\, of\,2nd\, and\,3rd\, numbers = (40+45)/2 =42.So, the first quartile (Q1) is17., the second quartile (Q2) is30, and the third quartile (Q3) is42..

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