# Range of the middle 75% of the data

• Nikki10
In summary, to find the kth percentile, you will need to calculate n*k/100 where k is the desired percentile and n is the number of observations. If given n*k/100 = value, you can solve for n by dividing the value by k/100. Then, use a z-table to find the appropriate z-value for the desired percentage and calculate the range of the middle percentage of the data using the formula mean +/- (z-value)(standard deviation).
Nikki10

## Homework Equations

TO find the kth percentile
=nk/100 (where k=kth percentile and n is the number of observations
Need n?

Given:
n(50)/100 = 9.3
n=18.6

Can n not be an integer?

Then I planned on plugging the n into the formula to solve
for the 75th percentile
n(75)/100 = range of the middle 75% of the data

Help

## The Attempt at a Solution

Last edited:
Welcome to Physics Forums.

You'll need to calculate a z-statistic and use a table for the Standard Normal curve (which should be in your statistics textbook.)

A few things you should calculate or think about first:

1. What is the standard deviation for the dosage?
2. What percentage lies above the middle 75%? What percentage lies below the middle 75%?

Thank you so much. I think I understand

I want the x value that cuts off the upper 75% of the curve
P(X>x) = 0.75

So I went to the z-table, and got a z value of 0.67 (using 0.251 inside the table, or should i use 0.248)

0.67 = x-9.1/2.14
x= .67(2.14) + 9.1
x= 10.54

therefore, the range of the middle 75% of the data is at most 10.54

Nikki10 said:
Thank you so much. I think I understand

I want the x value that cuts off the upper 75% of the curve
P(X>x) = 0.75

So I went to the z-table, and got a z value of 0.67 (using 0.251 inside the table, or should i use 0.248)
Not quite. Take a look at this figure:

If the middle (green part) of the area were 75%, what would be the areas of the white and yellow parts? And what would be the areas of the white+green combined?

0.67 = x-9.1/2.14
x= .67(2.14) + 9.1
x= 10.54

therefore, the range of the middle 75% of the data is at most 10.54
This part would be correct once you get the correct z-value to use.

Wait I think I have it now

There will be 12.5% between the mean and each Z-score,so we look for .125. The closest Z is .32, so the middle 75% is between Z = 0.32 and Z = -32.

Therefore, 9.1 - (0.32)(2.14) to 9.1 + (.32)(2.14) = 8.41 through 9.78.

Nikki10 said:
Wait I think I have it now

There will be 12.5% between the mean and each Z-score,...
Uh, no. There's 12.5% between each z-score and infinity.

Right, There will be 12.5% between infinity and each Z-score. There is 37.5% between each z-score and the mean

Don't i still look look for .125 making the middle 75% between Z = 1.15 and Z = -1.15. (from z-table)

Therefore, 9.1 - (1.15)(2.14) to 9.1 + (1.15)(2.14) = 6.61 through 11.6 making the range of the middle 75% of the data at most 4.99

Last edited:
Yes, that looks good.

Thank you

## What is the range of the middle 75% of the data?

The range of the middle 75% of the data is a measure of spread in a dataset. It represents the difference between the third quartile (Q3) and the first quartile (Q1) of the data.

## Why is it important to know the range of the middle 75% of the data?

Knowing the range of the middle 75% of the data helps us understand the spread of the data and the variability within the dataset. It can also give us insights into the distribution of the data.

## How do you calculate the range of the middle 75% of the data?

To calculate the range of the middle 75% of the data, we first need to find the third quartile (Q3) and the first quartile (Q1) of the data. Then, we simply subtract Q1 from Q3 to get the range.

## Can the range of the middle 75% of the data be negative?

Yes, the range of the middle 75% of the data can be negative. This occurs when the first quartile (Q1) is greater than the third quartile (Q3), resulting in a negative range value.

## How does the range of the middle 75% of the data differ from the total range of the data?

The range of the middle 75% of the data only considers the middle 75% of the data, while the total range of the data includes all data points. This means that the total range can be affected by extreme outliers, while the range of the middle 75% is more resistant to outliers.

Replies
1
Views
1K
Replies
6
Views
3K
Replies
7
Views
7K
Replies
6
Views
2K
Replies
2
Views
2K
Replies
6
Views
2K
Replies
1
Views
776
Replies
4
Views
2K
Replies
29
Views
3K
Replies
1
Views
1K