Question

use the formula for finding the kth percentile from the openstax text, section 2.3, measures of the location of the data. to find p_97, first find the locator? i = (dont round yet) use the locator, give the value for the 97 - percentile: p_97 = now use a spreadsheet to find the 97 - percentile: p_97 = question help: read video written example submit question

Explanation:

Step1: Recall percentile - locator formula

The formula for the locator $i$ of the $k$ - th percentile is $i=\frac{k}{100}n$, where $n$ is the total number of data points. However, since the total number of data points $n$ is not given in the problem - statement, we assume a general approach. If we assume we have all the necessary data from the histogram to calculate the cumulative frequencies. Let's assume we have $n$ data points. For $k = 97$, $i=\frac{97}{100}n=0.97n$.

Step2: Interpolation for percentile value

If $i$ is an integer, the $k$ - th percentile is the average of the data values in the $i$ - th and $(i + 1)$ - th ordered positions. If $i$ is not an integer, we round up to the next whole number. Let's assume we have the cumulative - frequency distribution from the histogram. We find the class interval in which the $i$ - th value lies. Then we use the interpolation formula $P_k = L+\frac{\frac{k}{100}n - cf}{f}\times w$, where $L$ is the lower limit of the class containing the $k$ - th percentile, $cf$ is the cumulative frequency of the class preceding the class containing the $k$ - th percentile, $f$ is the frequency of the class containing the $k$ - th percentile, and $w$ is the width of the class interval. But without specific data on frequencies, cumulative frequencies, and class - intervals from the histogram, we can't calculate a numerical value.
Since we are only asked for the locator first:

Answer:

$i = 0.97n$ (where $n$ is the total number of data points)
For the value of $P_{97}$, without more information from the histogram (such as class - intervals, frequencies, and cumulative frequencies), we can't provide a numerical answer. If we assume we are using a spreadsheet, we would input the data values, sort them, and then use the percentile function (e.g., in Excel, we can use the PERCENTILE.EXC or PERCENTILE.INC functions depending on the definition of percentiles we want to use). But again, without the actual data, we can't give a numerical value for $P_{97}$.