# Total Quality Management Questions and Answers – Statistics for TQMR – 2

This set of Total Quality Management Assessment Questions and Answers focuses on “Statistics for TQMR – 2”.

1. Measures of precision are also known as ___________
a) Measures of central tendency
b) Measures of dispersion
c) Measures of accuracy
d) Measures of statistics

Explanation: Measures of precision are also known as measures of dispersion. They determine the spread of the observations around the center. Range, mean deviation and standard deviation are the three measures of dispersion.

2. For symmetrical distribution, mean=median=mode.
a) True
b) False

Explanation: For symmetrical distribution, mean=median=mode. For asymmetrical distribution, mode=3*median-2*mean. So, if two parameters are known, the third one can be evaluated.

3. Given for an asymmetrical distribution, median=20, mean=22, what is the mode?
a) 12
b) 14
c) 16
d) 18

Explanation: For an asymmetrical distribution, mode=3*median-2*mean. Here, median=20 and mean=22. So, mode = 3(20)-2(22)=60-44=16.

4. Find the range of the following observations: 1,2,4,7,8,13.
a) 11
b) 12
c) 13
d) 14

Explanation: Range is the difference between the highest and lowest observation in a series. Here, the highest observation is 13 and the lowest observation is 1. So, range=13-1=12.

5. What is the mean deviation from the mean of the following observation:9,9,2,3,6,9,4?
a) 2.50
b) 2.62
c) 2.40
d) 2.57

Explanation: The mean of the given observation is (9+9+2+3+6+9+4)/7=6. Mean deviation from mean = (|6-9|+|6-9|+|6-2|+|6-3|+|6-6|+|6-9|+|6-4|)/7 = (3+3+4+3+0+3+2)/7=2.57.
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6. The square of the standard deviation is variance.
a) True
b) False

Explanation: The square of the standard deviation is variance. For example, if the variance of a given set of observations is 66.2, the standard deviation would be $$\sqrt{66.2}$$=8.13.

7. The standard deviation is 110 and the mean is 770. What is the coefficient of variation?
a) 15
b) 14.29
c) 13.37
d) 12

Explanation: The coefficient of variation is given by (SD/mean)*100. So, the coefficient of variation, in this case, is (110/770)*100 = 14.29.

8. If the coefficient of variation of a data set A is 40 and for data set B it is 60, which data set is more consistent?
a) Data set A
b) Data set B
c) Both are equally consistent
d) Neither of them is consistent

Explanation: The coefficient of variation represents the variability of a given set of observations. Therefore, the data set with less coefficient of variation is more consistent. Hence, data set A is more consistent compared to data set B.

9. If the variance of the data 2, 4, 5, 6, 8, 17 is 23.33. Then, what is the variance of 4, 8, 10, 12, 16, 34?
a) 40
b) 42.55
c) 46.66
d) 49

Explanation: When each observation in a given data set is multiplied by a constant, the variable also gets multiplied by the same constant. Here, the constant=2 and the original variance is 23.33. The new variance is 23.33*2=46.66.

10. A set of observations x1, x2, x3, x4, has a standard deviation = 6. Each of these observations is added with a constant k. What is the new standard deviation?
a) 10
b) 8
c) 6
d) 4

Explanation: When each observation of a given data set is increased by a constant k, the standard deviation remains unchanged. Hence, the standard deviation is 6.

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