Mean Practice Questions

Mean (also called the Arithmetic Mean or Average) is a measure of central tendency that represents the typical or central value of a dataset.

Question 1: A man keeps a record of the number of steps he jogs each day throughout the week. His step count for each day is recorded as follows:

• Monday: 8000
• Tuesday: 7500
• Wednesday: 8200
• Thursday: 7900
• Friday: 8100
• Saturday: 7800
• Sunday: 7700

Using this information, calculate the mean (average) number of steps he jogged per day

Solution:

The mean number of steps is shown in the graph below.

Sum of steps = 8000 + 7500 + 8200 + 7900 + 8100 + 7800 + 7700 = 54,200

Mean = 54,200 ÷ 7 = 7,886 steps

Question 2: Calculate the mean of the first 5 even natural numbers.

Solution: 

Given,

• Observed first 5 even natural numbers 2, 4, 6, 8, 10
• Total number of observed values = 5

Using Mean Formula

Mean = (Sum of observed values in data)/(Total number of observed values in data)

⇒ Sum of observed values = 2 + 4 + 6 + 8 + 10 = 30

Total number of observed values = 5
⇒ Mean = 30/5
⇒ Mean = 6 

Therefore, mean for first 5 even numbers = 6

Question 3: Calculate the mean of the first 10 natural odd numbers.

Solution: 

Given,

• Observed first 5 odd natural numbers 1, 3, 5, 7, 9.
• Total number of observed values = 5

Using Mean Formula

Mean = (Sum of observed values in data)/(Total number of observed values in data)

Sum of observed values = 1 + 3 + 5 + 7 + 9 = 25

Total number of observed values = 5

⇒ Mean = 25 / 5
⇒ Mean = 5

Therefore, mean for first 5 odd numbers = 5

Question 4: Calculate missing values from the observed set 2, 6, 7, x, whose mean is 6.

Solution:

Given,

• Observed values 2, 6, 7, x
• Number of observed values = 4
• Mean = 6

Using Mean Formula

Mean = (Sum of observed values in data)/(Total number of observed values in data)

⇒ Sum of observed values = 2 + 6 + 7 + x = 15 + x

Total number of observed values = 4

⇒ 6 = (15 + x)/4
⇒ 6 × 4 = 15 + x
⇒ x = 9

Therefore, missing value from the set is 9

Question 5: There are 20 students in Class 10. The marks obtained by the students in mathematics (out of 100) are given below. Calculate the mean of the marks.

Solution:

Given,

• Total number of students in class 10 = 20
• x₁ = 100, x₂ = 92, x₃ = 80, x₄ = 75, x₅ = 70
• f₁ = 1, f₂ = 3, f₃ = 5, f₄ = 10, f₅ = 1

Using Mean Formula

\bar{x} = \frac{f_1x_1 + f_2x_2 + f_3x_3 +...f_nx_n}{f_1+f_2+f_3...f_n}
⇒ x̄ = {(100 × 1) + (92 × 3) + (80 × 5) + (75 × 10) + (70 × 1)}/20
⇒ x̄ = (100 + 276 + 400 + 750 + 70)/20 
⇒ x̄ = 1596/20 = 79.8 marks

Question 6: Calculate the mean of the following dataset.

Solution:

Range of data is 60 to 76, for assumption of mean, lets take average of the range values,

Assumed Mean = (60 + 76) /2 = 136/2 = 68

Now, Let's A = 68 be assumed mean of the data,

Now, using assumed mean value, let's create the table for step deviation as follows:

Height (in inches)	Frequency(fi)	Class Mark (xi)	Deviation (di)	Step Deviation (ui)	fi × ui
60 - 62	2	61	-7	-3.5	-7
62 - 64	3	63	-5	-2.5	-7.5
64 - 66	4	65	-3	-1.5	-6
66 - 68	6	67	-1	-0.5	-3
68 - 70	5	69	1	0.5	2.5
70 - 72	3	71	3	1.5	4.5
72 - 74	1	73	5	2.5	2.5
74 - 76	1	75	7	3.5	3.5
	∑f = 25				∑fiui = -10.5

Thus, Mean = 68 + 2 × (-10.5)/25 
⇒ Mean = 68 + 2 × (-0.42) 
⇒ Mean = 68 - 0.84 = 67.16

Thus, mean height of data using step deviation method is 67.16 inches.

Thus, Mean = 68 + 2 × (-10.5)/25 

⇒ Mean = 68 + 2 × (-0.42) 

⇒ Mean = 68 - 0.84 = 67.16

Thus, the mean height of the data using the step deviation method is 67.16 inches.

Question 7: Heights of 100 students grouped into intervals:

Solution:

• Total frequency:

∑f_i = 12 + 28 + 35 + 25 = 100

• Sum of f_ix_i:

1710 + 4144 + 5355 + 3950 = 15159

xˉ = 15159/100 ​= 151.59 cm

So, the mean height of the 100 students is 151.59 cm.

Practice Questions

Question 1: Find the Mean temperature of a week given that the temperatures from Monday to Sunday are 21℃, 23℃, 22.5℃, 21.6℃, 22.3℃, 24℃, 20.5℃.

Question 2: Find the mean of the first 10 even numbers.

Question 3: Find the Mean height of students if the given heights are 150 cm, 152 cm, 155 cm, 160 cm, and 148 cm.

Question 4: Find the Mean of the given dataset