Question

The marks (out of 50) obtained by a group of students in a test in Mathematics are 35,26,40,35,9,18,6,45,31,25. Find
(i) the highest and the lowest marks obtained by students.
(ii) the range of the marks obtained.
(iii) the mean of the marks obtained by the group.

Answer 1

Hint: We will observe the value to find the highest and lowest value. Then, take the difference of the highest and the lowest value to find the range of the group. In the last part, we have to calculate the mean of the observations. We will find sum of observations and then use the formula, $\dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$ to find the mean of the given data.

Complete step-by-step answer:
The marks obtained by a group are 35,26,40,35,9,18,6,45,31,25.
Here, we can see the highest marks are 45 and the lowest marks are 6.
In part (ii) we have to find the range of the marks obtained.
The range is the difference of the highest and the lowest marks.
Hence, the range of the marks is 6 to 45.
Now, we find the mean of the marks obtained by the group.
We know that mean is given by $\dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$
The sum of observations is \[35 + 26 + 40 + 35 + 9 + 18 + 6 + 45 + 31 + 25 = 270\]
And the number of observations is 10.
On substituting these values, we will get,
$\dfrac{{270}}{{10}} = 27$
Hence, the mean of the observations is 27.

Note: The mean of the data calculates the central value of the data. It is also known as average. Students generally make mistakes in calculation part of the mean, so it has to be done carefully. The range of the data gives the difference between the highest and the lowest value.