onsider two data sets. (Refer to screensho

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Consider two data sets.

(Refer to screenshot)

Consider two data sets.
Set A: n = 5; x = 4
Set B: n = 50; x = 4
Σ
Σ
x = nx. To compute x for the new data set, add 20 to
x of the original
(a) Suppose the number 20 is included as an additional data value in Set A. Compute x for the new data set. Hint:
data set and divide by 6. (Round your answer to two decimal places.)
(b) Suppose the number 20 is included as an additional data value in Set B. Compute x for the new data set. (Round your answer to two decimal places.)
(c) Why does the addition of the number 20 to each data set change the mean for Set A more than it does for Set B?
O Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A.
O Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A.
O Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A.
O Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A.
Transcribed Image Text:Consider two data sets. Set A: n = 5; x = 4 Set B: n = 50; x = 4 Σ Σ x = nx. To compute x for the new data set, add 20 to x of the original (a) Suppose the number 20 is included as an additional data value in Set A. Compute x for the new data set. Hint: data set and divide by 6. (Round your answer to two decimal places.) (b) Suppose the number 20 is included as an additional data value in Set B. Compute x for the new data set. (Round your answer to two decimal places.) (c) Why does the addition of the number 20 to each data set change the mean for Set A more than it does for Set B? O Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A. O Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A. O Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A. O Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A.
Expert Solution
Step 1

The mean formula is,

x=xn

Now,

x=xn4=x5x=20

 Now, If one score of X = 20 is added to the sample, then n = 5+1=6. The value for the new mean is,

x=xnx=20+206x=6.66666x=6.67

Hence, the value for the new mean is 6.67.

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