all students in a pe class completed a basketball free throw shooting event and the highest number of shots made was 32. the next day a student who had transferred into the school completed the event, making 35 shots. indicate whether adding the new student's score to the rest of the data made each of these summary statistics increase, decrease, or stay the same for mean, median, range, IQR and standard deviation?

Question

all students in a pe class completed a basketball free throw shooting event and the highest number of shots made was 32. the next day a student who had transferred into the school completed the event, making 35 shots. indicate whether adding the new student's score to the rest of the data made each of these summary statistics increase, decrease, or stay the same for mean, median, range, IQR and standard deviation?

Answer 1

To determine whether adding the new student's score changes the summary statistics (mean, median, range, IQR, and standard deviation), we need to calculate the original and updated values of the statistics.

Let's start with the mean. The mean is calculated by summing up all the values and dividing by the total number of values.

Original mean:
To find the original mean, we need to know the scores of all the students in the class. If we have that information, we can add up all the scores and divide by the number of students.

Updated mean:
To find the updated mean, we add the new student's score to the original sum of scores and divide by the total number of students + 1 (including the new student).

If the updated mean is larger than the original mean, it has increased. If it's smaller, it has decreased. If the means are equal, it has stayed the same.

Similarly, we can follow a similar process for the other statistics.

Median:
The median is the middle value when the scores are arranged in numerical order. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.

Range:
The range is the difference between the maximum and minimum values.

IQR (Interquartile Range):
The IQR is the range between the first quartile (25% percentile) and the third quartile (75% percentile). It measures the spread of the central half of the data.

Standard Deviation:
The standard deviation is a measure of the dispersion or spread of the data. It quantifies how much the data deviates from the mean.

By calculating these statistics before and after the new student's score is added, we can determine whether each statistic has increased, decreased, or stayed the same.