As cars passed a checkpoint, the following speeds were clocked and recorded.
Speed (mph): 55 62 61 54 68 72 59 61 70
what's the range? , 1st quartile and 3rd quartile? please.
i found the range and min and max and 2nd quartile but my range 1st and 3rd quartile is wrong
mean*
To find the range, first you need to determine the minimum and maximum values in the given set of speeds.
Step 1: Find the minimum value
The minimum speed in the set is 54 mph.
Step 2: Find the maximum value
The maximum speed in the set is 72 mph.
Step 3: Calculate the range
The range is the difference between the maximum and minimum values.
Range = Maximum value - Minimum value
Range = 72 - 54
Range = 18 mph
Therefore, the range of the given set of speeds is 18 mph.
To find the first quartile (Q1) and the third quartile (Q3), you need to arrange the speeds in ascending order.
Step 1: Arrange the speeds in ascending order
55 59 61 61 62 68 70 72
Step 2: Determine the position of the first quartile (Q1)
To find the position of Q1, use the formula:
Position of Q1 = (n + 1) * 0.25
where n is the total number of data points.
In this case, n = 9, so:
Position of Q1 = (9 + 1) * 0.25
Position of Q1 = 2.5
Since the position is not a whole number, you need to take the average of the values at positions 2 and 3 to find Q1.
Q1 = (59 + 61) / 2
Q1 = 60 mph
Step 3: Determine the position of the third quartile (Q3)
To find the position of Q3, use the formula:
Position of Q3 = (n + 1) * 0.75
In this case:
Position of Q3 = (9 + 1) * 0.75
Position of Q3 = 7.5
Again, the position is not a whole number, so you need to take the average of the values at positions 7 and 8 to find Q3.
Q3 = (70 + 72) / 2
Q3 = 71 mph
Therefore, the first quartile (Q1) is 60 mph, and the third quartile (Q3) is 71 mph.