The marks( out of 100) obtained by a group of students in a Science test are 85, 76, 90, 85, 48, 56, 95, 81 & 75.Find the a) Find the Range of the marks obtained.
Answers
Answer:
1) The marks obtained by a group of students are 85, 76, 90, 85, 39, 48, 56, 95, 81, 75.
Now, arrange the marks in ascending order.
39, 48, 56, 75, 76, 81, 85, 85 , 90, 95
Here, we can see the last marks in the ascending order is 95 and the first marks are 39.
Hence, the highest marks are 95 and the lowest marks are 39.
2) The range is the difference between the highest and lowest marks.
Range = Highest Marks – Lowest Marks
Substitute the values,
⇒⇒Range =95−39=95−39
Subtract the values on the right side,
∴∴Range =56=56
Hence, the range is 56.
3) We know that mean is given by
Mean=Mean=Sum of Marks Number of studentsSum of Marks Number of students………...….. (1)
The sum of the marks is,
⇒39+48+56+75+76+81+85+85+90+95=730
⇒39+48+56+75+76+81+85+85+90+95=730
The number of students is 10.
Substitute these values in equation (1),
Mean =73010=73010
Cancel out the common factors,
∴∴Mean =73=73
Hence, the mean marks of the student are 73.
Note: The mean of the data calculates the central value of the data. It is also known as average. Students generally make mistakes in the 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.