13 Find the mean, mode and median for the following data: Classes 0-10 10-20 20-30 30-40 40-50 50-60 60-70 - Maths - Statistics

Question

13 Find the mean, mode and median for the following data:
Classes 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 5 8 15 20 14 8 5

Ajanta Trivedi · Accepted Answer

according to given observation:

mean = $\frac{Σ f x}{N} = \frac{2615}{75} = 34.866 \approx 34.87$

to find the median : we will apply the formula ;

median = $L + (\frac{\frac{N}{2} - F}{f}) * i$

75/ 2 = 37.5.

this lies in the interval 30-40.

i = size of the class interval

L = lower limit of the CI which includes the median score.

F = cumulative frequency up to median CI

f = frequency in the class interval that contains the median.

therefore L = 30 ; F = 28 ; f = 20 ; i =10

thus median = $30 + (\frac{37.5 - 28}{20}) * 10 = 30 + 4.75 = 34.75$

mode = $L + [\frac{f_{m} - f_{1}}{2 f_{m} - (f_{1} + f_{2})}] * i$

where

L = lower class boundary of modal class

$f_{m} =$ the frequency of the modal class

$f_{1} =$ previous frequency of the modal class

$f_{2} =$ the next frequency of the modal class

i = size of the modal class

modal class is the class with maximum frequency

from the observation: maximum frequency = 20.

modal class = 30-40

L = 30 ; $f_{m} =$ 20 ; $f_{1} =$ 15 and $f_{2} =$ 14 ; i = 10

mode = $30 + [\frac{20 - 15}{2 * 20 - (15 + 14)}] = 30 + [\frac{5}{40 - 29}]$

= 30 + (5/11)

= 30 + 0.4545

= 30.4545

hope this helps you.

cheers!!

13. Find the mean, mode and median for the following data: Classes 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 5 8 15 20 14 8 5