Answer:
a) Decrease
b) New mean = 78.43
c) Decrease
Step-by-step explanation:
We are given the following in the question:
Total number of students in class = 28
Average of 27 students = 79
Standard Deviation of 27 students = 6.5
New student's score = 63
a) The new student's score will decrease the average.
b) New mean
New mean =
Thus, the new mean is 78.43
c) Since the new mean decreases, standard deviation for new scores will decrease.
This is because the new value is within the usual values i.e. within two standard deviations of the mean. So, this wont cause a lot of variation as this value will be closer to already available data values. Also number of observations (n) in the denominator is increasing. Based on both these points we can conclude that standard deviation will decrease
Formula for Standard Deviation:
where are data points,
is the mean and n is the number of observations.
