Important Questions: Data Handling - Class 7 MCQ

Solution:

1. Add all the numbers: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

2. Count the total number of numbers: There are 10 numbers.

3. Divide the sum by the total number of numbers: Arithmetic mean = 55 / 10 = 5.5

Therefore, the arithmetic mean of 1, 2, ..., 9, and 10 is 5.5.
 

Shortcut for Finding the Mean of Consecutive Numbers

For a series of consecutive numbers, the arithmetic mean is simply the average of the first and last number.

In this case, the numbers are consecutive from 1 to 10.

• First number: 1
• Last number: 10

Mean = (First number + Last number) / 2 = (1 + 10) / 2 = 11 / 2 = 5.5

Therefore, the arithmetic mean of 1, 2, ..., 9, and 10 is 5.5.

This shortcut works because the numbers are evenly spaced.

By definition of average, the average daily sale = 

However, without calculating we can say that the answer is D since the average lies between the maximum and the minimum. 

Arranging the given data in ascending order, we have, 33, 35, 41, 46, 55, 58, 64, 77, 87, 90 and 92.
As there are 11 terms ie. odd (n+1)/2 ,  (11+1)/2 = 6 .The sixth entry is 58. 
∴ Median is 58.

The mean is representative of the whole group.  

Arithmetic mean = sum of observation / total no of observation

therefore;

Sum of observation = arithmetic mean x total no of observation

Sum of observation = 85 X 5=425

Since every apple has now 10g more, the average will rise by 10g, So accurate average= 52+10=62g

Mode occurs most frequently.  

Average height of the mountains 
= 

To find the median height, first arrange the heights in ascending order:

6000 m, 6500 m, 7500 m, 8200 m, 8600 m, 8800 m.

Since there are six values, the median is the average of the 3rd and 4th values:

(7500 + 8200) / 2 = 7850 m.

Ages: 26, 32, 38, 41, 26, 31, 35, 33, 26, 37

Calculate the sum of the ages: 26+32+38+41+26+31+35+33+26+37= 325

Count the number of ages: 10

Mean =  years.