Math Problem Statement

48.5 49.1 49.5 51.6 52 52 52.3 52.3 52.9 53.1 53.7 53.8 54.3 55 55.3 55.3 55.8 55.9 56 56.6 56.8 57 57.5 58.3 58.4 58.5 58.7 59 59.1 59.4 59.6 59.6 59.9 60.2 60.3 60.5 60.8 61 61.1 61.4 61.5 61.7 61.9 62 62 62.2 62.3 62.7 62.8 63.2 63.3 63.3 63.8 63.9 64 64.1 64.3 64.3 64.6 64.7 64.9 65 65.3 65.7 66.1 66.4 66.6 66.7 66.7 67.1 67.1 67.5 67.8 68 68.3 68.5 68.8 68.9 69.1 69.2 69.3 69.5 69.5 69.5 69.6 69.7 70 70.2 70.6 70.9 70.9 71 71 71 71.4 71.7 71.8 72.6 72.7 73.2 73.7 73.7 73.8 74.1 75 75.3 75.8 76.7 77.5 77.7 78.2 80.2 80.5 83.9 85.6 88 90.9

5 10 15 20 25 length (cm) 45 50 55 60 65 70 75 80 85 90 95 Frequency [Graphs generated by this script: setBorder(54,40,20,15); initPicture(40.5,95,0,28);axes(181.8,5,1,null,5); fill="blue"; stroke="black"; textabs([165,0],"length (cm)","above");line([45,-0.56],[45,0.56]); text([45,0],"45","below");line([50,-0.56],[50,0.56]); text([50,0],"50","below");line([55,-0.56],[55,0.56]); text([55,0],"55","below");line([60,-0.56],[60,0.56]); text([60,0],"60","below");line([65,-0.56],[65,0.56]); text([65,0],"65","below");line([70,-0.56],[70,0.56]); text([70,0],"70","below");line([75,-0.56],[75,0.56]); text([75,0],"75","below");line([80,-0.56],[80,0.56]); text([80,0],"80","below");line([85,-0.56],[85,0.56]); text([85,0],"85","below");line([90,-0.56],[90,0.56]); text([90,0],"90","below");line([95,-0.56],[95,0.56]); text([95,0],"95","below");textabs([0,115],"Frequency","right",90);rect([45,0],[50,3]);rect([50,0],[55,10]);rect([55,0],[60,20]);rect([60,0],[65,28]);rect([65,0],[70,25]);rect([70,0],[75,18]);rect([75,0],[80,7]);rect([80,0],[85,3]);rect([85,0],[90,2]);rect([90,0],[95,1]);]

To find P29, what is the value of the locator? Incorrect

Use the locator, give the value for the 29-Percentile: P29 = Incorrect

Solution

To find the 29th percentile (P29), let's go through the steps.

Step 1: Arrange the Data in Order

It seems the data you provided is already arranged in ascending order.

Step 2: Use the Formula for Percentile Locator

The locator for the PkP_k percentile is given by: L=k100×(n+1)L = \frac{k}{100} \times (n + 1) Where:

  • k=29k = 29 (since you want the 29th percentile),
  • nn is the number of data points.

Step 3: Calculate the Number of Data Points

Counting the values from the data set provided, there are 99 data points.

Step 4: Apply the Formula

L=29100×(99+1)=29100×100=29L = \frac{29}{100} \times (99 + 1) = \frac{29}{100} \times 100 = 29 So, the locator is 29, meaning the 29th data point in the list corresponds to the 29th percentile.

Step 5: Find the 29th Data Point

Looking at the sorted data set, the 29th data point is 58.7.

Thus, the 29th percentile (P29) is 58.7.

Would you like more details or clarifications on this method?


Here are 5 related questions to further explore the topic:

  1. What is the percentile formula for other percentiles (e.g., P50, P75)?
  2. How does the interpolation method work when the locator is not an integer?
  3. What is the difference between a percentile and a quartile?
  4. How can you calculate the percentile rank of a specific value within a data set?
  5. How do you interpret the meaning of the 29th percentile in real-world contexts?

Tip: When working with percentiles, if the locator isn't an integer, you usually interpolate between the two closest data points.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Percentile
Descriptive Statistics
Data Ordering

Formulas

Percentile Locator Formula: L = (k/100) × (n + 1)

Theorems

-

Suitable Grade Level

Grades 9-12