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

Step 1: Draw the frequency table for the given data.

The frequency table for the given data is

Step 2: Find the highest number.

Understand that from the frequency table it is clear that the highest number is $9$.

Step 3: Find the lowest number.

Understand that from the frequency table it is clear that the lowest number is$1$.

Step 4: Calculate the range of the data set.

Know that the difference between the highest and the lowest values in the data is called the range of the data.

Therefore, the range of the data set:

$\begin{array}{c}\text{Highest\hspace{0.17em}value}-\text{Lowest\hspace{0.17em}value}=9-1\\ =8\end{array}$

Step 4: Calculate the arithmetic mean.

Know that arithmetic mean is defined as the sum of the values of all observations divided by the number of observations.

Therefore, the arithmetic mean is:

$\begin{array}{c}\overline{X}=\frac{4+6+7+5+3+5+4+5+2+6+2+5+1+9+6+5+8+4+6+7}{20}\\ \overline{X}=\frac{100}{20}\\ \overline{X}=5\end{array}$

Hence,

(i) The number which is the highest is $9$.

(ii) The number which is the lowest is $1$.

(iii) The range of the data is $8$.

(iv)The arithmetic mean of the data is $5$.