##### Share this:

## STATISTICS

Is the study or the methods of collecting, summarizing and presenting data and interpreting the information.

MEASURES OF CENTRAL TENDENCY

1. Mean

2. Median

3. Mode

MEAN “X”

Is obtained by adding up all the data values then divide by the number of characters.

I.e.

i.e. =mean

x1+x2+x3………. Sum of observations

N =number of observation

Example

1. Find mean score from the following scores of biology test 10, 25, 45, 15,63 42,7

=

= 29.57

When the data is given with frequency or in grouped data;

= or

f= frequency

∑= summation

2. Find the mean number of children per family from the following table

2. Find the mean number of children per family from the following table

No. of children [x] | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

No. of families [f] | 3 | 6 | 7 | 8 | 10 | 12 | 8 | 4 | 2 |

Solution

Finding the mean of the numbers in the table below;

No. of children [x] | No. of families [f] | fx |

3 | 0 | |

1 | 6 | 6 |

2 | 7 | 14 |

3 | 8 | 24 |

4 | 10 | 40 |

5 | 12 | 60 |

6 | 8 | 48 |

7 | 4 | 28 |

8 | 2 | 16 |

Total | 60 | 236 |

= =

= 3.93

Exercise

1. Football club has the following number of goals scored against them 0,1,0, 2, 9,0 , 1, 2,1. What is the mean number of goals scored against them?

Class interval | Class mark [x] | Frequency [f] | fx |

91-95 | 93 | 0 | 0 |

86-90 | 88 | 1 | 88 |

81-85 | 83 | 6 | 498 |

76-80 | 78 | 10 | 780 |

73 | 15 | 1095 | |

66-70 | 68 | 34 | 2312 |

61-65 | 63 | 22 | 1386 |

56-60 | 58 | 10 | 580 |

51-55 | 53 | 2 | 106 |

N=100 | ∑fx=6845 |

Class interval | Class mark[x] | F | D=x-A | fd |

91-95 | 93 | 0 | 35 | 0 |

86-90 | 88 | 1 | 30 | 30 |

81-85 | 83 | 6 | 25 | 150 |

76-80 | 78 | 10 | 20 | 200 |

71-75 | 73 | 15 | 15 | 225 |

66-70 | 68 | 34 | 10 | 340 |

61-65 | 63 | 5 | 110 | |

56-60 | 58 | 10 | 0 | 0 |

51-55 | 53 | 2 | -5 | -10 |

Total | 100 | 1045 |

f | fx | |

61 | 10 | 610 |

64 | 20 | 1280 |

67 | 30 | 2010 |

70 | 15 | 1050 |

73 | 5 | 365 |

Total | 80 | 5315 |

Class mark | |

41-46 | 3 |

35-40 | 4 |

29-34 | 9 |

23-28 | 12 |

17-22 | 18 |

11-16 | 28 |

5-10 | 26 |

Class mark[x] | Frequency [f] | D= x-A | fd |

41-46 | 3 | 30 | 90 |

35-40 | 24 | 96 | |

29-34 | 9 | 18 | 162 |

23-28 | 12 | 12 | 144 |

17-22 | 18 | 6 | 108 |

11-16 | 28 | 0 | 0 |

5-10 | 26 | -6 | -156 |

Total | 100 | 444 |

Number of visits | frequency |

5 | 16 |

6 | 33 |

1 | 47 |

8 | 54 |

9 | 31 |

10 | 10 |

11 | 4 |

12 | 2 |

13 | 0 |

14 | 2 |

15 | 1 |

Number of visits[x] | Frequency [f] | Fx |

5 | 16 | 80 |

6 | 33 | 198 |

7 | 47 | 329 |

8 | 54 | 432 |

9 | 31 | 279 |

10 | 10 | 100 |

11 | 4 | 44 |

12 | 2 | 24 |

13 | 0 | 0 |

14 | 2 | 28 |

15 | 1 | 15 |

Total | 200 | 1529 |

Length [mm] | f | Cumulative frequency |

88-96 | 3 | 3 |

97-105 | 5 | 8 |

106-114 | 9 | 17 |

115-123 | 12 | 29 |

124-132 | 5 | 34 |

133-141 | 4 | 38 |

142-150 | 2 | 40 |

Total | 40 | 169 |

Marks | frequency | Cumulative frequency |

11-20 | 1 | 1 |

21-30 | 3 | 4 |

31-40 | 10 | 14 |

41-50 | 21 | 35 |

51-60 | 6 | 41 |

61-70 | 5 | 46 |

71-80 | 4 | 50 |

50 |

Class mark | frequency | Cumulative frequency |

3 | 3 | |

101 | 5 | 18 |

119 | 10 | 33 |

128 | 13 | 46 |

137 | 7 | 53 |

Total | 53 |

Class mark | frequency | Cumulative frequency |

15 | 0 | 0 |

20 | 5 | |

25 | 15 | 20 |

30 | 12 | 32 |

35 | 10 | 42 |

40 | 0 | 42 |

Height [cm] | 160 | 165 | 170 | 180 | 185 | |

frequency | 2 | 12 | 32 | 24 | 21 | 8 |

Height in [cm] | frequency | Cumulative frequency |

3 | 3 | |

165 | 12 | 15 |

170 | 32 | 47 |

175 | 24 | 71 |

180 | 21 | 92 |

185 | 8 | 100 |

total | 100 |

Class mark | frequency | Cumulative frequency |

15.5 | 1 | 1 |

25.5 | 3 | 4 |

35.5 | 10 | 14 |

45.5 | 21 | 35 |

55.5 | 41 | |

65.5 | 5 | 46 |

75.5 | 4 | 50 |

Total | 50 |

Wages in [TSHS} | frequency | Cumulative frequency |

55 | 8 | 8 |

65 | 10 | |

75 | 16 | 34 |

85 | 15 | 49 |

95 | 10 | 59 |

105 | 5 | 64 |

Total | 64 | |

Mass in kg | frequency | Cumulative frequency |

47 | 0 | |

47 | 0 | 0 |

52 | 16 | 16 |

51 | 20 | 36 |

62 | 14 | 50 |

61 | 12 | 62 |

72 | 8 | 70 |

77 | 6 | 76 |

82 | 4 | 80 |

87 | 0 | 80 |

Total | 80 | |

Height in cm | frequency |

82 | 10 |

85 | 11 |

88 | 14 |

91 | 10 |

94 | 9 |

97 | 6 |

Total | 60 |

## 1 Comment