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Diego wondered how far sixth-grade students could throw a ball. he decided to collect data to find out. he asked 10 friends to throw a ball as far as they could and measured the distance from the starting line to where the ball landed. the table shows the distances he recorded in feet.
40 76 40 63 47 57 49 55 50 53
find the median and iqr of the data set.
on a later day, he asked the same group of 10 friends to throw a ball again and collected another set of data. the median of the second data set is 49 feet, and the iqr is 6 feet.
did the 10 friends, as a group, perform better (or throw farther) in the second round compared to the first round? explain how you know.
were the distances in the second data set more variable or less variable compared to those in the first round? explain how you know.

Respuesta :

azikennamdi

The median of the number recorded in the question is 51.5 feet. This is obtained by dividing the sum of two numbers that occur centrally in half.

What is median?

The central value in a list ordered from smallest to largest is the median of a set of values.

What is the Inter-quartile Range (IQR) of an observation?

The formula for the Inter-quartile range is given as:

IQR = Q₃- Q₁ (that is Median of the Upper Half Less the Median of the lower half)

Step 1 - First, let's arrange the numbers sequentially

→  40, 40, 47, 49, 50, 53, 55, 57, 63, 76

Step 2 - Determine the upper and lower halves and their median

If the Lower half is  40, 40, 47, 49, 50, then it's median is 47

If the Upper half is   53, 55, 57, 63, 76, then its median is 57.

Hence:

IQR = 57 - 47

= 10 feet.

Given that the median of the second data set is 49 feet, and the IQR is 6 feet. Did the 10 friends, as a group, perform better (or throw farther) in the second?

No, the friends didn't perform better in the second round because the was a significant drop in the median and the IQR. The median dropped from 51.5 to 47 and the IQR from 10 to 6.


Were the distances in the second data set more variable or less variable compared to those in the first round?

It can be concluded that the distance in the second set of data is less variable when juxtaposed with those form the first set.

Learn more about Median at:
https://brainly.com/question/26151333
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