What is the value of the 30th percentile for the data set?
7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 6
To find the 30th percentile, you need to arrange the data set in ascending order.
1, 2, 3, 3, 4, 5, 6, 7, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20
Next, calculate the position of the 30th percentile. The 30th percentile can be found using the formula:
Position = (30 / 100) × (N + 1)
where N is the total number of data points.
In this case, N = 20, so
Position = (30/100) × (20 + 1) = 6.3
Since position 6.3 falls between the 6th and 7th data points, you need to interpolate to find the value corresponding to the 30th percentile.
30th percentile = value at position 6 + (position difference × (value at position 7 - value at position 6))
30th percentile = 6 + (0.3 × (7 - 6)) = 6 + 0.3 × 1 = 6 + 0.3 = 6.3
Therefore, the value of the 30th percentile for the given data set is 6.3.
are you sure
Apologies for the confusion. Let's recalculate the 30th percentile.
Since the total number of data points is 20, to find the position of the 30th percentile:
Position = (30 / 100) × (N + 1) = (30 / 100) × (20 + 1) = 0.3 × 21 = 6.3
The position 6.3 falls between the 6th and 7th data points.
To find the value at the 30th percentile, you can either use linear interpolation or the nearest-rank method.
Using linear interpolation:
30th percentile = value at position 6 + (position difference × (value at position 7 - value at position 6))
30th percentile = 6 + (0.3 × (7 - 6)) = 6 + 0.3 = 6.3
Using the nearest-rank method:
Since the position 6.3 is closer to position 6, the value at position 6 will be the 30th percentile. That is 6.
Therefore, the value of the 30th percentile for the given data set is 6.