(4)Ten studentsenrolled in a statistics class during the summer. The data below
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Question
(4)Ten studentsenrolled in a statistics class during the summer. The data below show the grades (%) obtained by the students in the midterm examination. Student Score 55 62 68 48 95 64 36 44 52 56 (a)Find the arithmetic mean, the median and the mode for this data set. (b)Given the results obtained in part (a) of this question, which measure would you consider the most appropriate as a description of central location? Explain. (c) Is there any observation that could be considered a possible or probable outlier in this data set? Explain with the aid of an appropriate statistical evaluation of the data set. (d)The rates of inflation for an economy over a period of 4 months are 1%, 1.5%, 1.02% and 1.7%. Find the average rate of inflation for the four months. Explain your choice of the measure of "average" you used in this specific case.Explanation / Answer
Arithmetic mean= Total of scores divided by number of observations
Total scores = 55 + 62 + 68 + 48 + 95 +64 + 36 +44 + 52 +56=580
Total observations=10
Artithmetic mean=580/10=58
Median
Arrange from lowerst to highest, the middle value is median. Since the list is a even number, the average of the middle numbers is the median.
36, 44, 48, 52, 55, 56, 62, 64, 68, 95
Median = (55+56)/2=55.5
Mode is the value than occurs the most.
No value occurs most frequently in the distribution, so there is no mode.
b) Mean is the best measure of central tendency since it takes into account all values and reflects the true average.
c)
An outlier is defined as being any point of data that lies over 1.5 IQRs below the first quartile (Q1) or above the third quartile (Q3) in a data set.
High = (Q3) + 1.5 IQR
Low = (Q1) – 1.5 IQR
Median is 55.5
Q1 is the middle number to the left of the median, which is 48
Q3 is the middle number to the right of the median, which is 64.
IQR= 64-48=16
High= 64 + 1.5 *16
Low= 48 - 1.5*16
High =64+24=88
Low= 48 -24=24
Any value above 88 or less than 24 are outliers.
95 is the upper end outlier.
d) We have to take the arthimetic mean to find out the average inflation rate.
Arithmetic mean = Total value in the data divided by number of observations
Since there are 4 months, the number of observations is 4
(1% +1.5%+1.02% +1.7%)/4
=5.22/4=1.305%
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