Find the Interquartile Range, Mode, Variance and Standard Deviation for given data

Question

Based on the given grouped data in the table in the attached image: https://ibb.co/1GhcbzB , for time taken for students travelling to their college,

how can I find

a) The Interquartile range

b) the mode

c) the variance and

d) the standard deviation

Answer 1

Hi Greene,

a. For quartiles, take:

Q1 = (n +1)/4 = (50 + 1)/4 = 12.75

Q3 = 3(n + 1)/4 = 3(50 + 1)/4 = 38.25

IQR = Q3 - Q1 = 38.25 - 12.75 = 25.5

b. Single mode value is not plausible and usually not relevant for grouped data--modal class is class with highest frequency, which is 11-20 minutes. If you need a single value, go with 15.5 minutes, the midpoint of this class.

c. and. d.

Variance = (1/n) [Sum (Fi (Xi - xbar)²]

Xi = Group midpoint

xbar = mean

n= sample size = 50

Example:

First, you need the mean. This is:

xbar = sum(xi*fi)/n

f= group frequency

xbar = (4.5*8) + (15.5*14) + (25.5*12) + (35.5*9) + (45.5*7) = 20.84

Then, for first example, you would do:

8(4.5-20.84)² = 2136

You would then need to do this for each class; then add up and divide by 50 (n). That's your variance. Then, take the square root of the result for standard deviation.