SD

• 142.5 3 162.5 136• 145 8 165 93• 147.5 15 167.5 42• 150 45 170 16• 152.5 90 172.5 6• 155 155 175 2• 157.5 194 M=160• 160 (M) 195 SD=5

SDWEIGHTS OF STUDENTS (Kg)

3 8 1545

90

155

194 195

136

93

4216 6 20

50

100

150

200

250

143 145 148 150 153 155 158 160 163 165 168 170 173 175

WEIGHT

N0. O

F ST

UDEN

TS

NORMAL DISTRIBUTION• Range, mean±1SD=160±5=155 to 165cm

– 68.27% of the observations• Range, mean±2SD=160±2x5=150 to

170cm– 95.45% of the observations

• Range, mean±3SD=160±3x5=145 to 175cm– 99.5% of the observations

• 3 observations < -3 SD & 2 observations > +3 SD fall in 0.05% group.

RELATIVE VARIATE (Z)

• Deviation from the mean in a normal distribution or curve is called relative or standard normal deviate.

• It is measured in terms of SD & it tells us how much an observation is higher or smaller than mean in terms of SD.

• Z= observation-mean =X-X¯ SD SD

RANGE

• Easy to understand• Easy to calculate• Useful as a rough measure of variation• Value may be greatly changed by an

extreme value• Highly unstable measure of variation.

MEAN DEVIATION

• Simple to understand and interpret.• Affected by the value of every

observation• Less affected by absolute variation• Not suited for any mathematical

treatment.

SD

• Affected by value of every observation• It avoids algebraic fallacy• Less affected by fluctuations of sampling

than other measures of dispersion• Has a definite mathematical meaning• Has a great practical utility in sampling

and statistical inferences.

QUESTION

• Average weight of baby at birth is 3.05Kg with SD of 0.39Kg. In a normal distributiona) wt. of 4 Kg as abnormal?b) wt. of 2.5 Kg as normal?

SAMPLING

• Not possible to include each & every member

• Not possible to examine all people of country

• To test efficacy of drug to all patients• Cooking of rice• Costly collection & Time consuming• Blood test

POPULATION

• Population• Sample• Parameter: a value calculated from a

population– Mean (μ)– Standard Deviation(σ)

• Sample– Mean (X)– Standard deviation ( s)

SAMPLING

• Sample is a part of population• Estimation of population parameters• To test the hypothesis about the

population from which the sample was drawn.

• Inferences are applied to the whole population but generalization are valid if sample size is sufficiently large & must be representative of the population-unbiased.

SAMPLING

• Sampling units are break down of population into smaller parts which are distinct and non overlapping so that each member / element of the population belongs to one and only one sampling unit.

• When a list of all individuals , households, schools and industries are drawn, it is called sampling frame.

Sample

• A representative sample is the one with which we can draw valid inference regarding the population parameters.

• It is representative of the population under study

• Is large enough but not too large• The selected elements must be properly

approached, included and interviewed.

Sample size• L= 2 σ √n

√n= 2 σ L

n= 4 σ² L²Example: 1.mean pulse rate=70

Pop. Standard deviation(σ)=8 beatsCalculate sample size?

2. Mean SBP=120,SD=10, calculate n?

Sample size

• Qualitative data

• N=4pq L²e.g.

SAMPLING TECHNIQUES• SIMPLE RANDOM SAMPLING• SYSTEMATIC SAMPLING• STRATIFIED SAMPLING• MULTISTAGE SAMPLING• CLUSTER SAMPLING• MULTIPHASE SAMPLING• CONVENIENT SAMPLING• QUOTA SAMPLING• SNOW BALL SAMPLING