Question

The difference between the maximum and minimum observations in the data is called _____.
A) mean of the data
B) range of the data
C) mode of the data
D) median of the data

Answer 1

In the given question, we have to choose the appropriate answer from the given options. Mean, range, mode and median are all part of statistics serving different purposes. Range is the difference between the highest and lowest data value in the set.

Complete step-by-step answer:
Let us understand the meaning of each measure to find out the correct answer:
Mean - The most popular indicator of central tendency is the mean. It simply reflects the average of the data set in question. It can be used to analyse both continuous and discrete data. It is equal to the sum of all the values in the collection of data divided by the total number of values.
For $n$ values in data set ${x_1},{x_2},...,{x_n}$ ,mean is calculated as follows:
$\bar X = \dfrac{{{x_1} + {x_2} + \ldots + {x_n}}}{n} = \dfrac{{\sum\limits_{i = 1}^n {{X_i}} }}{n}$
Range - In statistics, range is the difference between the highest and lowest data value in the set. Its formula is:
$Range = Highest\,value - Lowest\,value$
Mode - The most frequent number/observation occurring in the data set is known as the mode. In simple words, repetition of observation is mode. We can find it easily by looking at data set without any formula in case of discrete data. However, in case of grouped distribution we use the following formula:
$Mode = l + (\dfrac{{{f_1} - {f_0}}}{{2{f_1} - {f_0} - {f_2}}}) \times h$
Where,
$l$ = lower limit of the modal class
$h$ = size of the class interval
${f_1}$ = frequency of the modal class
${f_0}$ = frequency of the class preceding the modal class
${f_2}$ = frequency of the class succeeding the modal class
Median - median represents the mid value of the given set of data when arranged in a particular ascending or descending order.
If the number of values or observations in the given data is odd, then the median is given by ${(\dfrac{{n + 1}}{2})^{th}}$ observation. If in the given data set, the number of values or observations is even then the median is given by the average of ${(\dfrac{n}{2})^{th}}$ and ${(\dfrac{{n + 1}}{2})^{th}}$ observation i.e. $\dfrac{{{{(\dfrac{n}{2})}^{th}} + {{(\dfrac{{n + 1}}{2})}^{th}}}}{2}$.
After understanding the meaning, we can conclude that:
The difference between the maximum and minimum observations in the data is called range.

So, the correct answer is “Option B”.

Note: We often represent a set of data in statistics by a representative value that approximately defines the entire set of data. This representative value is called the measure of central tendency. The name implies that it is a value that the data is centred on.
Various parameters can be used to calculate central tendency, but the most widely used ones are mean, median and mode.