Short Quiz on Biostatistics- Measure of Dispersion, Standard deviation,Coefficient of variation

Instruction

1. This Test has 15 Questions
2. There is 1 Mark for each correct Answer

MCQ – 1

10 babies are born in a hospital on same day. All weigh 2.8 kg each; calculate the standard deviation:

Zero

One

Minus one

0.28

Explanation :

Standard deviation is used to measure deviation or dispersion.

In the above question all the babies weigh 2.8 kg and there is no question of dispersion to be measured.Hence the most appropriate answer will be zero.

Ref: Park’s Textbook of Preventive and Social Medicine By K. Park, 19th Edition, Page 701.

MCQ – 2

Median weight of 100 children was 12 kgs. The standard deviation was 3. Calculate the percent coefficient of variance:

25%

35%

45%

55%

Explanation :
Coefficient of variance = (SD/mean)×100

= (3/12)×100
= 25

Ref: Park 21st edition, page 787.

MCQ – 3

Mean deviation is –

Measure of dispersion

Measure of dispersion

A range

An average

Explanation :

Ans. is \’b\’ i.e., Measure of dispersion

Mean deviation is an absolute measure of variation or dispersion.

Mean deviation (MD)

• It is the average of the deviation from the arithmetic mean.

MD — E (x – )1) 11

o To calculate the mean deviation following steps to be followed –

• First calculate the arithmetic mean.

Then every single value is deducted from arithmetic mean to calculate deviation from mean (x – x).

Now each of these values of deviation from mean are added and then divided by the numbers of value (r1) to obtained mean deviation.

Example —> The diastolic blood pressure of 10 individuals is as follows – 83, 75, 81, 79, 71, 95, 75, 77, 84 and 90. The mean deviation is calculated :‑

Mean deviation

 Diastolic B.P. Arithmetic Mean Deviation from the mean (x – 83 81 2 75 81 -6 81 81 0 79 81 -2 71 81 -10 95 81 14 75 81 -6 77 81 -4 84 81 3 90 81 9

Total = 810                                                                Total = 56 (ignoring ± sign)

8 10                                    56

Mean = 10— 81    The Mean deviation     10— 5.6

MCQ – 4

Square root of deviation is also called as

Standard deviation

Standard error

Mean deviation

Range

Explanation :

Ans. is \’a\’ i.e., Standard deviation

o Standard deviation is square root of mean deviation, so it is also known as \”Root – means – square – deviation\”. o The steps for calculating SD are ‑

a)       First calculate mean (y)

b)       Then deduct this mean from each value to obtain deviation from mean (x – .T) as we did in calculating mean deviation (see above).

c)       Now square, each deviation (x – )7)2

d)       Add up the squared deviations —> S (x – 7)2

e)       Divide the result by the number of values (observations), i.e. n [or (n – 1) if the sample size is less than 30].

f)        At the end, take square root, which gives the standard deviation.

MCQ – 5

Correct relation between S = Standard deviation & V = Variance –

V = square root of S

S = Square root of V

V= 2S

S= 2V

Explanation :

Ans. is \’b\’ i.e., S = Square roof of V

MCQ – 6

Median weight of 100 children was 12 kgs. The Standard Deviation was 3.Calculate the percentage coefficient of variance –

25%

35%

45%

55%

Explanation :

Ans. is \’a\’ i.e., 25%

o We cannot calculate cofficient of variance here, because value of mean has not been provided (value of median is given).

o Only in standard normal curve mean = median.

o But in that case both are \’0\’ (In standard normal normal curve mean = median = mode = 0)

o I am clueless here.

o It you take, value of median as mean than the answer will be 25%.

MCQ – 7

Normal standard deviation true is-

Mean = Median

Mean > Medion

Median > Mean

Mode > Mean

Explanation :

Ans. is \’a\’ i.e., Mean = Medium

MCQ – 8

Mean and standard deviation can be worked out only if data is on –

Interval/Ratio scale

Dichotomous scale

Nominal scale

Ordinal scale

Explanation :

Ans. is \’a\’ i.e., Interval/Ratio scale

It is the arithmetic average of the individual values divided by the number of variables.

Thus quite logically, mean is useful only for quantitative variables (ie Interval and Ratio Scale data) which have got a measurable attribute.

o Standard Deviation

It\’s the measure of variance, calculated by method which everyone of us are well aware. It first involves findings out the mean value. Thus SD can only be worked out for quantitative data (Interval and ratio scales). o Now lets see other measures of central tendency and measures of variation.

MCQ – 9

Standard deviation does not depend on –

Mean

Median

Range

Sample size

Explanation :

Ans. is \’b\’ i.e. Median

MCQ – 10

If one wants to compare in two characteristics with variable difference, which measurement should be used?

Standard deviation

Percentile

Variance

Co-efficient of variation

Explanation :

Ans. is \’d\’ i.e. Co-efficient of variation

MCQ – 11

Standard deviation is defined as:

March 2009, March 2013 (a, c, f h)

Value of middle observation when data is arranged in ascending order.

Arithmetic mean

Dispersion of values about the mean

Most frequently occurring value

Explanation :

Ans. C: Dispersion of values about the mean

The steps are:

• Compute the mean for the data set.
• Compute the deviation by subtracting the mean from each value.
• Square each individual deviation.
• Add up the squared deviations.
• Divide by one less than the sample size.
• Take the square root.

Standard deviation gives us an idea of the spread of the dispersion; that the larger the standard deviation, the greater the dispersion of values about the mean.

MCQ – 12

Which of the following is used to compare two data sets taken on two different scales of measurement?

Variance

Coefficient of variation

Standard error of mean

Standard deviation

Explanation :

Ans. b. Coefficient of variation

MCQ – 13

Standard deviation is measured in ?

Distribution

Dispersion

Mean-deviation

All of the following

Explanation :

Ans. is \’b\’ i.e., Dispersion

MCQ – 14

In a group of 100 people, the average GFR is 85 ml/ min with a standard deviation of 25. What is the range for a 90% confidence interval?

81-89

80-90

75-95

70-100

Explanation :

Ans: A. 81-89

• The range for a 90% confidence interval in the given question is 81-89.

Confidence intervals:

• Lower limit & upper limit estimates for statistic given by:
• Lower Limit: statistic – C x SE (statistic).
• Upper Limit: statistic + C x SE.

Confidence coefficient:

• C = Confidence coefficient = 1.65 for 90% confidence interval.
• C= 1.96 for 95% confidence interval.
• C= 2.58 for 99% confidence interval.
• C = 3.29 for 99.9% confidence interval.

Now for a 90% confidence interval:

• Upper limit = 85 + (1.65 x 2.5) = 85 + 4 = 89.
• Lower limit = 85 + (1.65 x 2.5) = 85 – 4 = 81.
• Hence, for 90% confidence interval will 81-89.

MCQ – 15

1 SD covers 95% population

Normal standard deviate deviation from the mean in a normal distribution

Represent measurement of dispersions

It is better indicator of variability than range

Explanation :

Ans: b. Normal standard deviate deviation from the mean in a normal distribution c. Represent measurement of dispersions d. It is better indicator of variability than range[Ref Park 23rd/847-49, 21st/786;Biostatistics by BK Rao 2nd/54; Methods in Biostatistics by BK Mahajan 7th/57, 60-68; Basic eb, clinical Biostatisties 4th/30]

• Deviation from the mean in a normal distribution or curve is called relative or standard normal deviate or variate & is given the symbol Z. It is measured in term of SDs & indicates how much an observation is bigger or smaller than mean in unit of SD. So Z will be a ratio.
• The standard distribution curve (Normal distribution) is a perfectly symmetrical, bell shaped curve such that the mean, median and mode, all have the same value and coincide at the centre, Standard Distribution Curve (Normal)Q: Mean = Median = Mode