Question

Calculate the range and the coefficient of range with the following data:

Answer 1

Hint: Range is the difference between the highest and the lowest value of frequency for a given frequency distribution. the coefficient of range on the other hand is the ratio of difference between the highest and lowest value of frequency to the sum of highest and lowest value of frequency.

Complete step by step solution:
Now, in this question a frequency distribution table is given to us and we need to find the range and coefficient of range of the given data.

Now, the formula for Range is given as:
$Range = Highest value of Frequency - Lowest value of Frequency$
So, according to the question, from the frequency distribution table we can conclude that,
The Highest value of Frequency is 08 which belongs to the interval 30-40 and the lowest frequency value is 02 which belongs to the interval 0-10.
Then Range will now be given as:
$\
  Range = Highest value of Frequency - Lowest value of Frequency \\
   = 08 - 02 \\
   = 06 \\
\ $
So, Range = 6

Next, we need to calculate the coefficient of range
Now, Coefficient of Range is given as:
$CoefficientofRange = \dfrac{{Highest \space value \space of \space frequency - Lowest \space value \space of \space frequency}}{{Highest \space value \space of \space frequency + Lowest \space value \space of \space frequency}}...........(i)$
Now, as already concluded earlier from the table of data The Highest value of Frequency is 08 which belongs to the interval 30-40 and the lowest frequency value is 02 which belongs to the interval 0-10.
So,
\[\
  Highest \space value \space of \space frequency- Lowest \space value \space of \space frequency \\
   = 08 - 02 \\
   = 06................................................(ii) \\
\ \]
And,
\[\
  Highest \space value \space of \space frequency +Lowest \space value \space of \space frequency \\
   = 08 + 02 \\
   = 10...................................................(iii) \\
\ \]
Now, substituting the values from equation (ii) and (iii) in equation (i) we will get:
$\
  CoefficientofRange = \dfrac{{Highest \space value \space of \space frequency -Lowest \space value \space of \space frequency}}{{Highest \space value \space of \space frequency + Lowest \space value \space of \space frequency}} \\
   = \dfrac{6}{{10}} \\
   = 0.6 \\
\ $
Therefore, the coefficient of range is 0.6

Hence, the range is 6 and the coefficient of range is 0.6, for the given data.

Note: While calculating the coefficient of range one has to be careful to take the difference as numerator and sum as denominator, if taken otherwise then the value of coefficient will be wrong.