Median:
Arranging the given data in ascending order, we have: 110, 110, 120, 120, 120, 120, l30, l30, 140,140.
Number of data = 10, which is an even number.
\(\therefore \)Median = Mean of two middle values
\(\frac { 120+120 }{ 2 } \)=120
Mode: In the given data, we observe that the observation 120 occurs maximum number of times, i.e. 4 times.
\(\therefore \)Mode = 120

Sum of the observations (heights)
= [142 + 150 + 146 + 154 + 148] cm =740 cm
Number of observations = 5
\(\therefore \)Mean height = \(\frac { Sum\ of\ observations }{ Number\ of\ observations } \)
\(\frac { 140 }{ 5 } \) cm = 148 cm
Thus, the required mean height = 148 cm

Putting the data in a tabular form

Number	Tally-marks	Frequency
1		5
2	lll	8
3	lll	3
4		5
5	lll	3
6	ll	2
7	l	1

\(\because \)The frequency corresponding to 2 is the highest (i.e. 8)
\(\therefore \)The mode of the given set of data is 2.

Since 2 occurs 4 times
\(\therefore \) Mode of the given data is 2.
Note: For a set of given data mode can be more than one. For example, the mode of 5, 4, 3, 3, 3, 2, 2, 1,1 are 1 and 3.

(a)

(b) Tabulation of data.
(c) In India, children need sufficient protein food for nutrition.

Total number of balls
=3+6=9
(a) Probability of getting a red ball
\(=\frac{Total\ No.\ of\ red\ balls}{Total\ No.\ of balls}\)
\(=\frac{3}{9}=\frac{1}{3}\)
(b) Probability of getting a white ball
\(=\frac{Total\ No.\ of\ white\ balls}{Total\ No.\ of balls}\)
\(=\frac{6}{9}=\frac{2}{3}\)

In the given question,
Number of maximum outcomes = 5 (As there are five flashcards)
Favourable outcome, a flash card bearing 2
Hence,
\(Probability=\frac{No.\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}\)
\(=\frac{1}{5}\)

Frequency distribution table:

Given number are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 6 } \)
We know that, mean of two numbers always lies between them.
So, first rational number lying between \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 6 } \) can be found by calculating mean of \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 6 } \)
\(Mean=\frac { sum\quad of\quad all\quad observatins\qquad }{ number\quad of\quad observatins } \)
 = \(\frac { \frac { 1 }{ 3 } +\frac { 1 }{ 6 } }{ 2 } =\frac { \frac { 2+1 }{ 6 } }{ 2 } =\frac { \frac { 3 }{ 6 } }{ 2 } =\frac { 3\times 1 }{ 6\times 2 } =\frac { 3 }{ 12 } =\frac { 1 }{ 4 } ,so\frac { 1 }{ 3 } <\frac { 1 }{ 4 } <\frac { 1 }{ 6 } \)
We can find, one more rational number lying between \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 6 } \) by calculating mean of \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \)
\(Mean\quad =\quad \frac { \frac { 1 }{ 3 } +\frac { 1 }{ 4 } }{ 2 } =\frac { \frac { 4+3 }{ 12 } }{ 2 } =\frac { \frac { 7 }{ 12 } }{ 2 } =\frac { 7\times 1 }{ 12\times 2 } =\frac { 7 }{ 24 } \)
\(\therefore\)  \(\frac { 1 }{ 3 } <\frac { 7 }{ 24 } <\frac { 1 }{ 4 } <\frac { 1 }{ 6 } \)

Double bar graph of given data is as follows

The difference in the scale of the two language books in individual year is as follows:

Clearly, the difference in the scale of the two language books was least in the year 1998

(i) On arranging the data in ascending order, we get 12,12,13,13,14,14,14,16,19.
Here, 14 occurs more frequently i. e. 3 times.
\(\therefore\) Mode =14
(ii) Here, ascending order of the given data is 12,12,13,13,14,14,14,16,19
Since, the middle observation of the data = 14
\(\therefore\) Median of data = 14
Hence, mode = 14 and median = 14

On arranging the adjacent data in descending order, we get

Here, total rainfall
= 0.0+ 12.2+ 2.1 + 0.0+ 20.5+ 5.5+ 1.0= 41.3 mm
Number of days = 7
\(\therefore\) Mean rainfall = \(\frac { total\quad rain\quad fall }{ number\quad of\quad days } =\frac { 41.3 }{ 7 } =5.9mm\)
Hence, mean rainfall for the week is 5.9 mm

B played in all the four games, therefore his mean is calculated by adding all the points in four games and then dividing by 4
\(\therefore\) Mean = \(\frac { sum\ of\ points\ in\ four\ game }{ number\ of\ games } =\frac { 0+8+6+4 }{ 4 } =4.5\)
Hence, the required mean is 4.5

The frequency table is shown below.

It is clear from the table that, the highest number = 9

We know that, there are seven days in a week. Let the sleeping hours during a week are as follows:

Now, sum of the sleeping hours of one week
=8+7+6+7+6+7+8=49h
and number of days in a week = 7
Mean = \(\frac { total\ sleeping\ hours }{ total\ number\ of\ days } =\frac { 49 }{ 7 } =7h\)
Hence, the mean of your sleeping hours during Cine week is 7 h.