Question

The following data are the oxygen uptakes (milliliters) during incubation of a random
sample of 15 cell suspensions:
14.0, 14.1, 14.5, 13.2, 11.2, 14.0, 14.1, 12.2, 11.1, 13.7, 13.2, 16.0, 12.8, 14.4, 12.9.
Calculate all measures of Central tendencies and measures of dispersion.

Answer 1

Solution :-

we know that, Central tendencies are mean , median and mode .

so,

→ Arranging data in ascending order = 11.1, 11.2, 12.2, 12.8, 12.9, 13.2, 13.2, 13.7, 14.0, 14.0, 14.1, 14.1, 14.4, 14.5, 16.0 .

then,

→ Mean = sum of all data/15 = 201.4/15 = 13.4

→ Median = since n is odd , (n + 1)/2th term = (15+1)/2 = 8th term = 13.7

→ Mode = most frequent data = 13.2(2 times) , 14.0(2 times) and 14.1(2 times.)

now, measures of dispersion are range , variance and standard deviation .

so,

→ Range = maximum value - minimum value = 16.0 - 11.1 = 4.9

now,

→ sum of (mean - xi)² = (13.4 - 11.1)² + (13.4 - 11.2)² + (13.4 - 12.2)² + (13.4 - 12.8)² + (13.4 - 12.9)² + (13.4 - 13.2)² + (13.4 - 13.2)² + (13.4 - 13.7)² + (13.4 - 14.0)² + (13.4 - 14.0)² + (13.4 - 14.1)² + (13.4 - 14.1)² + (13.4 - 14.4)² + (13.4 - 14.5)² + (13.4 - 16.0)² = 23.02

then,

→ variance = sum of (mean - xi)²/n - 1 = 23.02/14 = 1.644

and,

→ standard deviation = √(variance) = √(1.644) = 1.28 .

Learn more :-

calculate the median and mode from the following income between (rs)100-200 100-300 100-400 100-500 100-600 no of person...

https://brainly.in/question/23585381

Some students of class X donated for the welfare of old age persons. The contributions are shown in the following distri...

https://brainly.in/question/17314012