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

**Instruction**

2. There is 1 Mark for each correct Answer

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

**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.**

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

**Ref:**Park 21st edition, page 787.

Mean deviation is –

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}

Square root of deviation is also called as *‑*

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.

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

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

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

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%.

Ans. is \’a\’ i.e., Mean = Medium

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

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.

Ans. is \’b\’ i.e. Median

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

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

Standard deviation is defined as:

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

**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.

Ans. b. Coefficient of variation

Standard deviation is measured in ?

Ans. is \’b\’ i.e., Dispersion

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?

**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.

**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