What are the minimum, first quartile, median, third quartile, and maximum of the data set?
40, 7, 2, 35, 12, 23, 18, 28
i can get the minimum and maximum and the median but not the first and third quartile
Quartiles mark each 25% of a set of data.
The first quartile Q1 is the 25th percentile
The second quartile Q2 is the 50th percentile
The third quartile Q3 is the 75th percentile
The second quartile Q2 is the median of data set and it divides data set into upper and lower halves.
The first quartile Q1 is the median of the lower half not including the value of Q2.
The third quartile Q3 is the median of the upper half not including the value of Q2.
Calculate Quartiles:
Order your data set from lowest to highest values.
2 , 7 , 12 , 18 , 23 , 28 , 35 , 40
Q2 split the ordered data set into two halves.
Find the median.
In this case median is ( 18 + 23 ) / 2 = 20.5
This is the second quartile Q2.
Q2 = 20.5
The lower quartile Q1 is the median of the lower half of the data.
2 , 7 , 12 , 18
In this case:
Q1 = ( 7 + 12 ) / 2 = 19 / 2 = 9.5
The upper quartile Q3 is the median of the upper half of the data.
23 , 28 , 35 , 40
In this case:
Q3 = ( 28 + 35 ) / 2 = 63 / 2 = 31.5
To find the first quartile (Q1) and third quartile (Q3), you need to sort the data set in ascending order first:
2, 7, 12, 18, 23, 28, 35, 40
To find the median (Q2), locate the middle value in the sorted data set. Since there are 8 values in the data set, the median is the average of the two middle values (23 and 28), which is 25.5.
To find Q1, you need to find the median of the lower half of the data set. In this case, the lower half is: 2, 7, 12, 18. The median of this subset is the average of the two middle values (7 and 12), which is 9.5. Therefore, Q1 is 9.5.
To find Q3, you need to find the median of the upper half of the data set. In this case, the upper half is: 23, 28, 35, 40. The median of this subset is the average of the two middle values (28 and 35), which is 31.5. Therefore, Q3 is 31.5.
So, the minimum is 2, Q1 is 9.5, Q2 (median) is 25.5, Q3 is 31.5, and the maximum is 40.
To find the first quartile and third quartile, you will need to sort the data set in ascending order.
The given data set after sorting in ascending order is:
2, 7, 12, 18, 23, 28, 35, 40
To find the median, you need to find the middle value of the data set. Since there are 8 values, the middle two values are 18 and 23. So, the median is (18 + 23) / 2 = 20.5.
To find the first quartile, you need to find the median of the lower half of the data set. The lower half of the data set consists of the values 2, 7, 12, and 18. Since there are 4 values, the middle two values are 7 and 12. The first quartile is (7 + 12) / 2 = 9.5.
To find the third quartile, you need to find the median of the upper half of the data set. The upper half of the data set consists of the values 23, 28, 35, and 40. Since there are 4 values, the middle two values are 28 and 35. The third quartile is (28 + 35) / 2 = 31.5.
Therefore, the minimum is 2, the first quartile is 9.5, the median is 20.5, the third quartile is 31.5, and the maximum is 40.