What are the minimum, first quartile, median, third quartile, and maximum of the data set? As cars passed a checkpoint, the following speeds were clocked and recorded. Speed (mph): 55 62 61 54 68 72 59 61 70
first, sort the numbers:
54 55 59 61 61 62 68 70 72
The min,median,max should now be obvious.
Now divide into 4 equal groups to see the quartiles.
To find the minimum, first quartile, median, third quartile, and maximum of a given data set, you need to arrange the data in ascending order.
The given data set is: 55, 62, 61, 54, 68, 72, 59, 61, 70.
Step 1: Arrange the data in ascending order:
54, 55, 59, 61, 61, 62, 68, 70, 72.
Now, we can find the minimum, first quartile, median, third quartile, and maximum.
Step 2: Find the minimum:
The minimum is the smallest value in the data set. Therefore, the minimum speed is 54 mph.
Step 3: Find the first quartile (Q1):
The first quartile is the median of the lower half of the data set. In other words, it is the value that separates the first 25% of the data from the remaining 75%. Since our data set has 9 values, we can find the position of the first quartile using the formula:
Position of Q1 = (25/100) * (N+1) = (25/100) * (9+1) = 2.5
The position is between the 2nd and 3rd values, so we take the average of these two values:
Q1 = (59 + 61) / 2 = 60 mph.
Step 4: Find the median (Q2):
The median is the middle value of the data set when arranged in ascending order. Since our data set has an odd number of values (9), the median is the value in the middle position, which is the 5th value:
Median = 61 mph.
Step 5: Find the third quartile (Q3):
The third quartile is the median of the upper half of the data set. It is the value that separates the first 75% of the data from the remaining 25%. Following the same calculation as for the first quartile, we have:
Position of Q3 = (75/100) * (N+1) = (75/100) * (9+1) = 7.5
Again, the position is between the 7th and 8th values, so we take the average:
Q3 = (68 + 70) / 2 = 69 mph.
Step 6: Find the maximum:
The maximum is the largest value in the data set. Therefore, the maximum speed is 72 mph.
In conclusion, the minimum, first quartile, median, third quartile, and maximum of the data set are as follows:
Minimum: 54 mph
First quartile (Q1): 60 mph
Median (Q2): 61 mph
Third quartile (Q3): 69 mph
Maximum: 72 mph