for a particular sample of 77 scores on a psychology exam the following results were obtained:
first quartile=44
third quartile= 71
standard deviation=6
range=45
mean= 64
median= 57
mode = 92
midrange=60
answer each of the following:
a) what score was earned by more students than any other scores? why?
b) what was the highest score?
c) what was the lowest score?
d)according to Chebysheve's theorem, how many students scored between 40 and 88?
e) assume that the distribution is normal. based on the empirical rule, how many students scored between 46 and 82?
* please show all calculations. i don't know where to begin. help, help, help. thank you.
mary
for a particular sample of 77 scores on a psychology exam the following results were obtained:
first quartile=44
third quartile= 71
standard deviation=6
range=45
mean= 64
median= 57
mode = 92
midrange=60
answer each of the following:
a) what score was earned by more students than any other scores? why?
b) what was the highest score?
c) what was the lowest score?
d)according to Chebysheve's theorem, how many students scored between 40 and 88?
e) assume that the distribution is normal. based on the empirical rule, how many students scored between 46 and 82?
* please show all calculations.
a) To determine the score earned by more students than any other score (mode), no explicit calculation is required, as the mode is given in the information provided. The mode in this case is 92, which means that more students have earned a score of 92 than any other score.
b) To find the highest score, you can use the range. The range is the difference between the highest and lowest scores. In this case, the range is given as 45, so the highest score can be calculated by adding the range to the lowest score.
highest score = lowest score + range
= 44 + 45
= 89
Therefore, the highest score is 89.
c) The lowest score is already given in the information provided, which is 44.
d) According to Chebyshev's theorem, for any data set (regardless of the shape of the distribution), at least (1 - 1/k^2) of the data will fall within k standard deviations from the mean. In this case, we are interested in the number of students who scored between 40 and 88.
The standard deviation is given as 6. Using Chebyshev's theorem, we can find how many students scored within 2 standard deviations from the mean.
k = 2
1 - 1/k^2 = 1 - 1/2^2 = 1 - 1/4 = 3/4
Therefore, at least 3/4 of the students scored within 2 standard deviations from the mean. We can calculate the number of students using the mean and standard deviation.
Lower limit = mean - (k * standard deviation) = 64 - (2 * 6) = 64 - 12 = 52
Upper limit = mean + (k * standard deviation) = 64 + (2 * 6) = 64 + 12 = 76
So, according to Chebyshev's theorem, at least 3/4 of the students scored between 40 and 88.
e) The empirical rule applies to data that follows a normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
In this case, we can calculate the number of students who scored between 46 and 82 based on the mean and standard deviation.
Lower limit = mean - (2 * standard deviation) = 64 - (2 * 6) = 64 - 12 = 52
Upper limit = mean + (2 * standard deviation) = 64 + (2 * 6) = 64 + 12 = 76
According to the empirical rule, approximately 95% of the students scored between 46 and 82.