Question

Organize the following marks in a class assessment, in a tabular form.
\[4,6,7,5,3,5,4,5,2,6,2,5,1,9,6,5,8,4,6,7\]
i). Which number is the highest?
ii). Which number is the lowest?
iii). What is the range of the data?
iv). Find the arithmetic mean.

Answer 1

Hint: In this question, we have given the marks of the assignment of a class. We have to represent the data in tabular form and find which number is highest, lowest, range of data and mean of the data given. So, we have to use the formula of range and mean of the data.
\[range = \text{highest number} - \text{lowest number}\]
\[\text{Mean} = \dfrac{\text{Sum of all the numbers}}{\text{Total number of terms}}\]

Complete step-by-step solution:
Given,
The data of the marks of the class in an assignment is,
\[4,6,7,5,3,5,4,5,2,6,2,5,1,9,6,5,8,4,6,7\]
To find,
Highest number, lowest number , range, average of the number
Formula used:
\[\text{Mean} = \dfrac{\text{Sum of all the numbers}}{\text{Total number of terms}}\]
Range= highest number-lowest number
The tabular form of the given data is

marks	frequency
\[1\]	\[1\]
\[2\]	\[2\]
\[3\]	\[1\]
\[4\]	\[3\]
\[5\]	\[5\]
\[6\]	\[4\]
\[7\]	\[2\]
\[8\]	\[1\]
\[9\]	\[1\]

i). highest number
Highest number: the maximum number that is got by the student is the highest number.
\[\text{Highest number} = 9\]
ii). lowest number
lowest number: a minimum number that is got by the student is the lowest number.
 \[\text{Lowest number} = 1\]
iii). Range of the data
The range of the data is given the difference between the highest number and the lowest number.
\[ \Rightarrow \text{Range} = \text{Highest number} - \text{Lowest number}\]
\[\text{Range} = 9-1\]
\[\text{Range} = 8\]
iv). Mean of the given number
\[mean = \dfrac{\text{Sum of all the numbers}}{\text{Total number of terms}}\]
On putting all the values from the data
\[\text{Mean} = \dfrac{{4 + 6 + 7 + 5 + 3 + 5 + 4 + 5 + 2 + 6 + 2 + 5 + 1 + 9 + 6 + 5 + 8 + 4 + 6 + 7}}{{20}}\]
On further calculating,
\[\text{Mean} = \dfrac{{100}}{{20}}\]
On dividing both the terms
\[mean = 5\]
Mean of the given data \[4,6,7,5,3,5,4,5,2,6,2,5,1,9,6,5,8,4,6,7\] is,
\[ \Rightarrow mean = 5\]

Note: In the given question we have to use the concept of the highest value, lowest value, range of the data, and mean of the data. You may commit a mistake in using the formula of range and mean. Mean is the average of the data. You may also commit mistakes in the calculation for finding the mean of the given data.