Measure of Central Tendency

Q.

What are the advantages and disadvantages of geometric mean ?

Q. A card is drawn from the set of 52 cards. Find the probability of getting a queen card.

1. 2/13
2. 1/26
3. 4/13
4. 1/13

Q.

Complete the following sentence : "Mode is the _________"

1. Most frequent value

2. Least frequent value

3. Middle most value

4. Average value

Q.

The average marks of the students in Mathematics of class $8^{th}$ is 45. But most of the students were given 60 out of 100.The Median of the class would be:

1. 30

2. 40

3. 50

4. 60

Q. Draw the graph of modulus function and describe it ?

Q. If Median = Mode + $x$ (Mean - Mode), then find the value of $x$.

1. 3
2. 2
3. $\frac{1}{3}$
4. $\frac{2}{3}$

Q.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality.
Find the median of the data.

$\begin{array}{cc}\text{Monthly consumption (in units)}& \text{Numbers of customers}\\ 65-85& 4\\ 85-105& 5\\ 105-125& 13\\ 125-145& 20\\ 145-165& 14\\ 165-185& 8\\ 185-205& 4\end{array}$

1. 140

2. 147

3. 137

4. 132

Q.

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.

$\begin{array}{cccccccc}\text{Weight(in Kgs)}& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ \text{Number of students}& 2& 3& 8& 6& 6& 3& 2\end{array}$

Q.

Find the mode and median of the following frequency distribution:
$\begin{array}{ccccccc}x& 10& 11& 12& 13& 14& 15\\ f& 1& 4& 7& 5& 9& 3\end{array}$

Q. Find the median for the following frequency distribution.

$\begin{array}{cc}Ageinyears& Numberofpeople\\ 15& 3\\ 16& 8\\ 17& 10\\ 18& 10\\ 19& 5\\ 20& 4\end{array}$

1. 17

Q. If the mean and mode of a data set are 2 and 5 respectively, find the median of a data set.

1. 5
2. 2
3. 3
4. 4
   

Q.

The following table shows the literacy rate (in percentage) of cities.

Literacy rate in $\%$	more than $30$	more than $35$	more than $40$	more than $45$	more than $50$	more than $55$	more than $60$	more than $65$	more than $70$
No. of cities	$40$	$32$	$21$	$16$	$12$	$8$	$6$	$4$	$3$

Draw a more than type ogive for the given data. Hence, obtain the median Literacy rate.

Q.

For finding mean by assumed mean method

$\overline{x}$ = $a+\frac{(\sum f\times d)}{\sum f}$

What does $d$ and $f$ indicate in the formula?

1. Difference between class mark and assumed frequency, assumed mean
2. Assumed mean, difference between class mark and assumed mean
3. Difference between class mark and assumed mean, frequency
4. Difference between class mark and assumed mean, assumed frequency

Q.

Complete the following sentence: "Mode is_______."

1. Middle most value

2. Average value

3. Least frequent value

4. Most frequent value

Q.

Find the median of the following data:$$\begin{array}{cccccccc}\text{Class interval}& 25-35& 35-45& 45-55& 55-65& 65-75& 75-85& 85-95\\ \text{Frequency}& 12& 16& 17& 15& 8& 19& 13\end{array}$$

1. 58.33
2. 54.3
3. 32.33
4. 51.67

Q.

100 surnames were randomly picked up from a local telephone directory & the frequency distribution of the number of letters in the English alphabets in the surname was obtained as follows.

$\begin{array}{ccccccc}\text{Number of letters}& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ \text{Number of surnames}& 6& 30& 40& 16& 4& 4\end{array}$
Determine the median number of letters in the surnames.

1. 8.05

Q. If the mean of $x_1$ and $x_2$ is $M_1$ and that of $x_1,x_2,x_3,x_4$ is $M_2$, then the mean of $a{x}_1,a{x}_2,\frac{x_3}{a},\frac{x_4}{a}$
is _____.

1. $\frac{a{M}_1+\left(\frac{M_2}{2}\right)}{2}$
2. $\frac{1}{2a}\left[\right(a^2-1)M_1+M_2]$
3. $\frac{1}{2a}\left[2\right(a^2-1)M_1+M_2]$
4. $\frac{M_1+M_2}{2}$

Q.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality.
Find the median of the data.

$\begin{array}{cc}\text{Monthly consumption (in units)}& \text{Numbers of customers}\\ 65-85& 4\\ 85-105& 5\\ 105-125& 13\\ 125-145& 20\\ 145-165& 14\\ 165-185& 8\\ 185-205& 4\end{array}$

1. 140

2. 147

3. 137

4. 132

Q. Calculate the mean of the distribution given below using the shortcut method.

marks	11-20	21-30	31-40	41-50	51-60	61-70	71-80
number of students	2	6	10	12	9	7	4

Q.

Three friends A, B and C started a business by investing a total sum of ₹ 22, 000. At the end of the year. A, B and C receives ₹ 900, ₹ 900 and ₹ 400 respectively as their profit share. What is the amount of capital invested by A, B and C?

1. Capital invested by A = ₹ 4000
   Capital invested by B = ₹ 9000
   Capital invested by C = ₹ 4000

2. Capital invested by A = ₹ 9000
   Capital invested by B = ₹ 7000
   Capital invested by C = ₹ 4000

3. Capital invested by A = ₹ 9000
   Capital invested by B = ₹ 9000
   Capital invested by C = ₹ 4000

4. Capital invested by A = ₹ 9000
   Capital invested by B = ₹ 3000
   Capital invested by C = ₹ 7000

Q. Daily wages of 50 workers of a factory are given below:-
Daily wages in Rs :- Workers
100 - 120 12
120 - 140 f
140 - 160 8
160 - 180 6
180 - 200 10
Find the missing frequency and hence find the mean daily wage of the workers.

Q.

For finding mean by assumed mean method

$\overline{x}$ = $a+\frac{(\sum f\times d)}{\sum f}$

What does $d$ and $f$ indicate in the formula?

1. Assumed mean, difference between class mark and assumed mean
2. Difference between class mark and assumed mean, assumed frequency
3. Difference between class mark and assumed mean, frequency
4. Difference between class mark and assumed frequency, assumed mean