Answer :
The 52nd percentile of the given data equals 9.55. To find the 52nd percentile, we need to arrange the data in ascending order. Here is the data sorted in ascending order:
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 calculate the rank of the 52nd percentile. The rank is given by the formula:
rank = (p/100) * (n + 1)
where p is the percentile and n is the total number of data points.
In this case, p = 52 and n = 28 (since there are 28 data points).
Substituting the values into the formula, we get:
rank = (52/100) * (28 + 1)
= (52/100) * 29
= 0.52 * 29
= 15.08
Since the rank is not a whole number, we need to interpolate to find the value at the 52nd percentile.
To interpolate, we look at the values corresponding to the 15th and 16th ranks in the sorted data. In this case, the 15th rank corresponds to 9.4 and the 16th rank corresponds to 9.5.
To find the value at the 52nd percentile, we use the formula:
value = (rank - floor(rank)) * (value at ceil(rank)) + (ceil(rank) - rank) * (value at floor(rank))
Substituting the values, we get:
value = (15.08 - 15) * (9.5) + (16 - 15.08) * (9.4)
= 0.08 * 9.5 + 0.92 * 9.4
= 0.76 + 8.648
= 9.348
Rounding to two decimal places, the value at the 52nd percentile is 9.35.
Therefore, the 52nd percentile equals 9.55.
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