Important Questions: Data Handling - Free MCQ Test with solutions for

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.

Step 1 Note the daily sales: 75, 120, 12, 50, 70.5, 140.5

Step 2 Find the total sales
75 + 120 = 195
195 + 12 = 207
207 + 50 = 257
257 + 70.5 = 327.5
327.5 + 140.5 = 468

So total = 468 litres

Step 3 Number of days = 6

Step 4 Average = Total ÷ Number of days = 468 ÷ 6 = 78 litres

Step 5 Therefore the correct option is d) 78 l

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 a measure that represents the overall value of a group of numbers.

• It is calculated by adding all observations together and dividing by the number of observations.
• The mean provides a general idea of the average value within a dataset.
• It is particularly useful when you want to summarise a large set of data.

However, it's important to note that the mean can be affected by extreme values, known as outliers, which may skew its representation of the data.

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 is a statistical term that refers to the value that appears most frequently in a data set.

• It represents the most common value.
• Unlike the mean or median, the mode is not affected by extreme values.
• In some data sets, there may be more than one mode, making it multimodal.

Overall, the mode is a useful measure for understanding the frequency of values within a data set.

Average height of the mountains 
= 

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.