Question 1: If the heights of persons are and respectively, find the mean height.

Answer:

Question 2: Find the mean of and .

Answer:

Question 3: Find the mean of first five natural numbers.

Answer:

Question 4: Find the mean of all factors of .

Answer:

Factors of are

Therefore

Question 5: Find the mean of first even natural numbers.

Answer:

First even natural numbers:

Therefore

Question 6: Find the mean of .

Answer:

Question 7: Find the mean of first five multiples of .

Answer:

First five multiples of are

Therefore

Question 8: Following are the weights (in kg) of new born babies in a hospital on a particular day: . Find the mean .

Answer:

Question 9: The percentage of marks obtained by students of a class in mathematics are: . Find their mean.

Answer:

Question 10: The numbers of children in families of a locality are: . Find the mean number of children per family.

Answer:

Question 11: If is the mean of and , prove that .

Answer:

Question 12: Duration of sunshine (in hours) in Amritsar for first days of August 1997 as reported by the Meteorological Department are given below: .

i) Find the mean ii) Verify that

Answer:

i)

ii)

Question 13: Explain, by taking a suitable example, how the arithmetic mean alters by (i) adding a constant to each term, (ii) subtracting a constant from each them, (iii) multiplying each term by a constant and (iv) dividing each term by a non-zero constant .

Answer:

i) We have

Let be the mean of observations . Then

ii) We have

Let be the mean of observations . Then

iii) We have

Let be the mean of observations . Then

iv) We have

Let be the mean of observations . Then

Question 14: The mean of marks scored by students was found to be . Later on it was discovered that a score of was misread as . Find the correct mean.

Answer:

Given:

(Let us assume was the incorrect entry)

Hence Correct Mean

Question 15: The traffic police recorded the speed (in km/hr) of motorists as . Later on an error in recording instrument was found. Find the correct overage speed of the motorists if the instrument recorded less in each case.

Answer:

We will use Property 5: If is the mean of observations, then the mean of the observations is , where is any real number.

Hence the correct

Question 16: The mean of five numbers is . If one number is excluded, their mean is . Find the excluded number.

Answer:

Given:

Let us assume that the excluded number is

… … … … … i)

Also

… … … … … ii)

From i) and ii) we get

Question 17: The mean weight per student in a group of students is . The individual weights of of them (in kg) are and . Find the weight of the seventh student.

Answer:

Given:

Question 18: The mean weight of numbers is . if each number is multiplied by , what will be the new mean?

Answer:

We will use Property 3: If is the mean of then the mean of is , where is any number different from zero. i.e. is each observation is multiplied by a non zero number , then the mean is also multiplied by .

Question 19: The mean of numbers is . If one number is excluded, their mean is . Find the excluded number.

Answer:

Given:

Let us assume that the excluded number is

… … … … … i)

Also

… … … … … ii)

From i) and ii) we get

Question 20: The mean of items was . Later on it was discovered that the two items were misread as and instead of and . Find the correct mean.

Answer:

Given:

(Let us assume was the incorrect entry)

Hence Correct Mean

Question 21: Find the values of and in each of the following cases:

i) and

iii) and

Answer:

i) … … … … … i)

… … … … … ii)

Subtract ii) from i) we get

Substituting in i) we get

Therefore

ii) … … … … … i)

… … … … … ii)

Subtract ii) from i) we get

Substituting in i) we get

Therefore

Question 22: The sums of the deviations of a set of values measured from and are and respectively. Find the value of and mean.

Answer:

… … … … … i)

… … … … … ii)

Subtract ii) from i) we get

Substituting in i) we get

Therefore

Question 23: Find the sum of the deviations of the variate values from their mean.

Answer:

Property 1: If is the mean of observations, , then . i.e. the algebraic sum of deviations from mean is zero.

Hence the answer is .

Question 24: If is the mean of the ten natural numbers show that

Answer:

We have

Now rearranging we get

Question 25: If the mean of the observations is find the value of .

Answer: