Question

1. Which of the following statements is correct?

a. The median can be strongly influenced by just one or two very low or high values.

b. The mode gives equal consideration to even very extreme values in the data.

c. There will be just one value for the mean, median , and mode in the data set.

d. The mean is able to make the most complete use of the data when compared to the median and mode.

e. None of these choices are correct.

2. Which of the following is not a correct statement?

a. Chebyshev's theorem applies only to normal distributions.

b. For distributions that are bell-shaped and symmetric, about 68% of the observations will fall within one standard deviation of the mean.

c. The coefficient of variation allows us to compare two sets of data based on different measurement units.

d. Standardized values have no units of measure.

e. The vertical line within the box in the box-and-whisker plot represents the median.

4. Which of the following statements is true regarding the normal distribution?

a. The mean is less than the mode, which in turn is less than the median.

b. The mean is less than the median and the median is less than the mode.

c. The mean is greater than the mode, which in turn is greater than the median.

d. The mean is greater than the median and the median is greater than the mode.

e. There is no difference in the values of the mean, median, and mode.

6. For a set of data, the mean is 50 and the standard deviation is 10. In the raw data, one of the observations is equal to 74. After the data are standardized, what will be the standardized value of this observation?

a. +7.4

b. -7.4

c. +2.4

d. -2.4

7.The numerical value of the coefficient of determination r ²

a. is the proportion of the variation in the independent variable x that is explained by the best-fit linear equation.

b. is the proportion of the variation in the dependent variable y that is explained by the best-fit linear equation.

c. indicates the direction of the relationship between the dependent variable y and the independent variable x.

d. Both "is the proportion of the variation in the dependent variable y that is explained by the best-fit linear equation" AND "is the proportion of the variation in the independent variable x that is explained by the best-fit linear equation" are correct.

e. is the proportion of the variation in the dependent variable y that is explained by the best-fit linear equation," AND "is the proportion of the variation in the independent variable x that is explained by the best-fit linear equation," AND "indicates the direction of the relationship between the dependent variable y and the independent variable x" are all correct.

Answer 1

Q 1. Property of mean

1. The sum of the deviations of each value from the mean is always zero.

2. it includes every value in your data set as part of the calculation.

3. it produces the lowest amount of error from all other values in the data set.

from 2 properties option d is the right answer.

Q2. Chebyshev's theorem applies to all data set, not only normally distributed data sets. According to this theory, the portion of any set of data within K standard deviations of the mean is always at least 1-1/K², K >1.

Q.4 The mean, median, and mode of a normal distribution are equal. This is because the normal distribution curve is symmetric and unimodal means has only one peak.