Answer :
The percentile for the data value 111 is 37.5 or 37.5th if you round down.
A percentile is a measure that represents a specific percentage of data points that fall below it in a dataset. The nth percentile in a dataset is defined as the value that is greater than n% of the data points. The percentile is a useful tool for determining how a given data point compares to the rest of the data.
For example, if a student scored in the 90th percentile on a standardized test, it means that they scored higher than 90% of all the other students who took the test. How to find the percentile? The formula for finding the percentile rank of a data point in a dataset is given as follows:
P = (number of data points below the given value / total number of data points) × 100
where:
P is the percentile rank expressed as a percentage. The number of data points below the given value is the number of data points in the dataset that are less than the given value.
The total number of data points is the total number of data points in the dataset. Using the given data set, we can calculate the percentile for the data value 111 as follows: There are 6 data points in the dataset that are less than 111.
Therefore, the number of data points below the given value is 6. The total number of data points in the dataset is 16.
Therefore, the total number of data points is 16. The percentile rank of 111 in the dataset is:
P = (number of data points below the given value / total number of data points) × 100P = (6 / 16) × 100P = 37.5.
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The percentile for the data value 111 is 13.33%.
The given data set is: 114, 126, 118, 112, 120, 122, 112, 110, 112, 114, 118, 128, 110, 114, 116.
For finding the percentile for the data value 111, firstly, we need to find the rank of this value among the other data values.
To do this, we can sort the data set in ascending order:
110, 110, 112, 112, 112, 114, 114, 116, 118, 118, 120, 122, 126, 128
The data value 111 is not present in the given data set.
Therefore, we can find its rank by taking the average of the ranks of the two data values between which it would lie.
111 would lie between the data values 110 and 112. These two values have ranks 1 and 3 respectively.
Therefore, the rank of 111 would be:
Rank of 111 = (1 + 3)/2
= 2
This means that the value 111 is at the 2nd position when the data set is sorted in ascending order.
Now we can use the following formula to find the percentile of the data value 111:
Percentile = (Number of values below the given data value / Total number of values) × 100
We can see that there are 1 + 1 = 2 values below 111. (Two values because the data value 110 is repeated.)
The total number of values in the data set is 15.
Therefore, Percentile = (2/15) × 100
= 13.33%
Therefore, the percentile for the data value 111 is 13.33%.
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