1. Consider the following three data sets A, B and C. A = {9,10,11,7,13} B = {10
ID: 3374598 • Letter: 1
Question
1. Consider the following three data sets A, B and C.
A = {9,10,11,7,13}
B = {10,10,10,10,10}
C = {1,1,10,19,19}
a) Calculate the mean of each data set.
A – 10
B-10
C-10
b) Calculate the standard deviation of each data set.
A- 2.2361
b- 0
C - 9
c) Which set has the largest standard deviation?
C is the highest
d) Is it possible to answer question c) without calculations of the standard deviation?
No. You can’t state which is the highest without knowing the standard deviation.
e) What are the mode and median for each data set?
A – No Mode. Median = 10.
B- 10 mode. Median = 10.
C- Mode 1,19 repeats twice
2. A given data set has a mean ? and a standard deviation ?.
a) What are the new values of the mean and the standard deviation if the same constant k is added to each data value in the given set? Explain.
b) What are the new values of the mean and the standard deviation if each data value of the set is multiplied by the same constant k? Explain.
3. If the standard deviation of a given data set is equal to zero, what can we say about the data values included in the given data set?
?(X-X)2 V (n -1) sum of all values Mear total number of values Median middle value (when the = where: data are arranged in order) X = each score X-the mean or average nthe number of values ? means we sum across the values Mode most common valueExplanation / Answer
1. mean for each dataset:
A: (9+10+11+7+13)/5 = 10
B: (10+10+10+10+10)/5 =10
C: (1+1+10+19+19)/5 = 10
2. Standard deviation for each data set:
A)
sum of (x-x')2 = 20
(x-x')2 /n-1 = 20/4 = 5
square root of this is standard deviation = 2.236
similarly for B and C
B: standard deviation = 0
C: Standard deviation = 9
3. C has highest standard deviation.
4. Yes, in the given sets of data we can tell easily that C has highest standard deviation as compared to others. we can see values are highly deviated from mean in C.
No. Data x-x' (x-x')2 1 9 -1 1 2 10 1 1 3 11 0 0 4 7 -3 9 13 3 9Related Questions
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