Solution
David answered on
Dec 22 2021
Q.1
n=68, First quartile, Q1 = 57, Third quartile, Q3 = 89, Standard deviation, = 7, Range = 60, Mean =
70, Median = 73, Mode = 74, Midrange = 68
To find,
1. What score was earned by more students than any other score? Why?
Sol. The score which occurs maximum number times, is the score which is earned by more students
than any other score. Mode is the value which occurs most frequently in a set of observations. Thus
value of mode, i.e. 74 is the score which was earned by more students than any other score.
2. What was the highest score earned on the exam?
Let, maximum value be M and minimum value be denoted by m,
Now, Range = maximum value – minimum value = 60
Therefore, M-m=60
Mid-Range= (Maximum value + minimum value)/2=68
Therefore,
= 68,
M + m=136
M-m=60
Adding above two equation,
2M = 196
M=196/2 = 98
m= 98-60 = 38
thus, Maximum value= 98, minimum value = 38
Therefore, highest score earned on the exam = 98
3. What was the lowest score earned on the exam?
Sol. Lowest score earned on the exam =minimum value = 38, as calculated in the above question.
4. According to Chebyshev’s Theorem, how many students scored between 42 and 98?
Sol: Mean-k * standard deviation = 42, i.e. = 70 – k*7=42
70-42=7*k
K=28/7=4
Mean + k* standard deviation = 98
70+k*7=98
K*7=98-70
K=28/7 =4
Now, from chebychev’s inequality, at least
) of the measurements will fall within
(mean-k*standard deviation, mean +k*standard deviation)
=
=
=
Thus, number of values falling between 42 and 98 =
=
= 63.75
Thus 63 values lie between 42 and 98.
5. Assume that the distribution is normal. Based on empirical rule, how many students scored
etween 63 and 77?
Sol. Let X be a random variable denoting the marks obtained by students.
We have to find the number of students who have scored between 63 and 77.
We find the probability of marks falling between 63 and 77, i.e. P(63
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