Answer :
The value of the 99th percentile for the given data is 14.3. The 99th percentile value is approximately 13.55.
To calculate the 99th percentile, we need to arrange the data in ascending order first:
4.9 5.1 6.3 6.7 7.0 7.1 7.8 8.6 8.7 8.8 8.9 9.0 9.4 9.4 9.5 9.6 9.9 10.0 10.1 10.1 10.1 10.3 10.4 10.7 10.9 11.3 11.6 11.8 14.3
Next, we need to find the rank of the 99th percentile. The rank can be calculated using the formula: rank = (p/100) × (n+1), where p is the percentile and n is the number of data points.
In this case, p = 99 and n = 29 (since there are 29 data points).
rank = (99/100) × (29+1)
= 0.99 × 30
= 29.7
Since the rank is not a whole number, we need to interpolate to find the value. We can use the formula:
value = L + (C - L) × f,
where L is the lower value, C is the upper value, and f is the fractional part of the rank.
Looking at the data, we can see that the 29th and 30th values are 11.8 and 14.3 respectively.
L = 11.8,
C = 14.3,
f = 0.7
value = 11.8 + (14.3 - 11.8) × 0.7
= 11.8 + 2.5 × 0.7
= 11.8 + 1.75
= 13.55
Therefore, the 99th percentile value is approximately 13.55.
The 99th percentile is a measure that represents the value below which 99% of the data falls. In other words, it indicates the value at which only 1% of the data is greater.
To find the 99th percentile, we first arrange the data in ascending order. Then, we calculate the rank of the percentile using the formula (p/100) * (n+1), where p is the percentile and n is the number of data points.
In this case, the rank is not a whole number, so we need to interpolate to find the value. We use the formula value = L + (C - L) × f,
where L is the lower value,
C is the upper value,
f is the fractional part of the rank.
By substituting the values into the formulas, we find that the 99th percentile value is approximately 13.55.
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