Which of the following is not true regarding the advantages

Which of the following is not true regarding the advantages of the mean as a measure of location?

     The mean is relatively insensitive to skewness in data?

a.) The mean is relatively insensitive to skewness in data?

b)     The mean uses all the values in the data set.

c)     The mean is uniquely defined for a given set of data.

d)    All of the above are true.

A resort hotel is interested in how far people travel to reach the hotel. Eight guests are interviewed, and each is asked the distance (in miles) from their home to the hotel. The resulting data is given below.

80        850     120     200     210     50       25       190

13.Suppose the investigator finds out that the number 85 was recorded wrongly as 850. If we use the correct number (85) in our computations which of the following statistics will be affected more?

a.Mean

b)Median

c)Mode

d)None of the above  

13.Scores on a standardized exam have a mean of 120 and standard deviation of 15. What z-score corresponds to test score of 150?

a)-2

b.) 2

c)-1

d)3

e)None of the above

The area under the standard normal for Z< -2.25 is:

a).975

b.).0125

c).0122

d).0119

e)None of the above

Solution

1)

The correct answer to the first problem is option A. Mean is actually very sensitive to the skewness in the data. Mean would shift if the data becomes positively or negatively skewed.

The other two statements are correct as mean uses all the values and is unique for a given data set.

2)

The mode is undefined for this data set as these point observations have no repeating values.As for the other values, the calculations are shown with the percentage changes in mean and median

3)

Z-score = X - mean / S.d

Thus,

Mean = 120, SD = 15, X = 150

Z = (150-120) / 15

= 30/15

= 2

4)

This can be directly read from a standard normal table with negative values given.

P (Z < -2.25) = 0.0122

In case only positive values are given,

P(Z < -2.25) = 1 - P (Z < 2.25 )

which again give the same answer

Hope this helps. Ask if you have any doubts.