Data Handlings

Find the range of heights of any ten students of your class.

Heights of 10 students of our class.

= 125, 130, 134, 137, 138, 139, 140, 143, 147, 150

We know

Range = Highest value – Lowest value

The highest value = 150cm

The lowest value = 125 cm

Then,

Range of Heights = Highest value – Lowest value

= 150 – 125

= 25 cm

Organise the following marks in a class assessment, in a tabular form.

4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7

(i) Which number is the highest? (ii) Which number is the lowest?

(iii) What is the range of the data? (iv) Find the arithmetic mean.

On Arranging in ascending order.

= 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 9

Now, we will draw the frequency table of the given data.

< img class="mathsPageImg" src="/Pathanto/image/cl7-3-9.jpg" >(i) From table the highest number is 9.

(ii)From table the lowest number is 1.

(iii) We know that

Range = Highest value – Lowest value

= 9 – 1 = 8

iv)Mean =
(Sum of all observations)
/
(Total number of observation)

Then,

Sum of all observation = 1 + 2 + 2 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7

+ 8 + 9 = 100

Total Number of Observation = 20

Mean =
100
/
20

= 5

The first five Whole numbers are 0, 1, 2, 3, and 4.

Mean =
(Sum of all observations)
/
(Total number of observation)

Then,

Sum of the numbers = 0 + 1 + 2 + 3 +4 = 10

Total Number = 5

Mean =
10
/
5

= 2
58, 76, 40, 35, 46, 45, 0, 100. Find the mean score.

(Sum of all scores)
/
(Total number of innings)

Total runs scored by the cricketer = 58 + 76 + 40 + 35 + 46 + 45 + 0 + 100 = 400

Total number of innings = 8

Then,

Mean =
400
/
8

= 50
Player | Game
1 |
Game
2 |
Game
3 |
Game
4 |

A | 14 | 16 | 10 | 10 |

B | 0 | 8 | 6 | 4 |

C | 8 | 11 | Did not Play | 13 |

Now answer the following questions:

(i) Find the mean to determine A’s average number of points scored per game.

(ii) To find the mean number of points per game for C, would you divide the total points by 3 or by 4? Why?

(iii) B played in all the four games. How would you find the mean?

(iv) Who is the best performer?

Total points scored by A in 4 games
/
Total number of games

=
(14 + 16 + 10 + 10)
/
4

50
/
4

= 12.5
(ii) To find the mean number for player C, we will divide the total points by 3. Because C played only 3 games.

(iii)We will divide the total points by 4 to find out the mean of B played

Then,

Mean of player B =
Total points scored by B in 4 games
/
Total number of games

=
(0 + 8 + 6 + 4)
/
4

=
18
/
4

= 4.5
(vi) Mean of player C =

Total points scored by C in 3 games
/
Total number of games

=
(8 + 11 + 13)
/
3

=
32
/
3

= 10.67
As we saw average points scored A more than B and C.

So A is the best performer among three.

85, 76 90, 85, 39, 48, 56, 95, 81 and 75.

Find the:

(i) Highest and the lowest marks obtained by the students.

(ii) Range of the marks obtained

(iii) Mean marks obtained by the group.

Arrange in ascending order,

= 39, 48, 56, 75, 76, 81, 85, 85, 90, 95

(i) The highest marks obtained by the student = 95

The lowest marks obtained by the student = 39

(ii) Range = Highest marks – Lowest marks

= 95 – 39 = 56

(iii) Mean of Marks =
Sum of all marks of students
/
Total number of students

=
39 + 48 + 56 + 75 + 76 + 81 + 85 + 85 + 90 + 95
/
10

=
730
/
10

= 73
1555, 1670, 1750, 2013, 2540, 2820.

Find the mean enrolment of the school for this period.

Sum of all observations
/
Number of observations

(1555 + 1670 + 1750 + 2013 + 2540 + 2820)
/
6

=
12348
/
6

= 2058
Day | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |

Rainfall
(in mm) |
0.0 | 12.2 | 2.1 | 0.0 | 20.5 | 5.5 | 1.0 |

(i) Find the range of the rainfall in the above data.

(ii) Find the mean rainfall for the week.

(iii) On how many days was the rainfall less than the mean rainfall.

(i) Range = Highest rainfall – Lowest rainfall

= 20.5 – 0.0= 20.5 mm

(ii) Mean of rainfall =
Sum of all observations
/
Number of observation

=

0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0
/
7

=

41.3
/
7

= 5.9 mm
(iii) Monday, Wednesday, Thursday, Saturday and Sunday the rainfall was less than the average rainfall.

135, 150, 139, 128, 151, 132, 146, 149, 143, 141.

(i) What is the height of the tallest girl? (ii) What is the height of the shortest girl?

(iii) What is the range of the data? (iv) What is the mean height of the girls?

(v) How many girls have heights more than the mean height.

On Arranging in ascending order,

128, 132, 135, 139, 141, 143, 146, 149, 150, 151

(i) The height of the tallest girl is 151 cm

(ii) The height of the shortest girl is 128 cm

(iii) Range = Tallest height – Shortest height

= 151 – 128 = 23 cm

(iv) Mean height of the girls =
Sum of height of all the girls
/
Number of girls

128 + 132 + 135 + 139 + 141 + 143 + 146 + 149 + 150 + 151
/
10

1414
/
10

= 141.4 cm
(v) There 5 girls who's heights more than the 141.4 cm