8. The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
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 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?
Answer:
(i) Range of rainfall = Highest rainfall – Lowest rainfall
= 20.5 – 0.0
= 20.5 mm
(ii) Mean of rainfall = Sum of all observations / Number of observations
= (0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0)/ 7
= 41.3/7
= 5.9 mm
(iii) We may observe that for 5 days, i.e. Monday, Wednesday, Thursday, Saturday and Sunday, the rainfall was less than the average rainfall.
9. The heights of 10 girls were measured in cm, and the results are as follows:
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?
Answer:
First, we have to arrange the given data 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 of given data = Tallest height – Shortest height
= 151 – 128
= 23 cm
(iv) Mean height of the girls = Sum of the 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) 5 girls have heights more than the mean height (i.e. 141.4 cm).
10. The scores on the Mathematics test (out of 25) of 15 students are as follows:
19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20
Find the mode and median of this data. Are they the same?
Answer:
Arranging the given scores in ascending order, we get
5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 20 occurs a maximum number of times.
Hence, the mode of the given sores is 20.
Median
The value of the middle-most observation is called the median of the data.
Here, n = 15, which is odd.
Where n is the number of students.
∴ median = value of 1/2 (n + 1)th observation
= 1/2 (15 + 1)
= 1/2 (16)
= 16/2
= 8
Then, the value of the 8th term = 20
Hence, the median is 20.
Yes, both values are the same.
11. The runs scored in a cricket match by 11 players are as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?
Answer:
Arranging the runs scored in a cricket match by 11 players in ascending order, we get
6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
Mean
Mean of the given data = Sum of all observations / Total number of observations
= (6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120)/ 11
= 429/11
= 39
Mode,
Mode is the value of the variable which occurs most frequently.
Clearly, 15 occurs a maximum number of times.
Hence, the mode of the given sores is 15.
Median,
The value of the middle-most observation is called the median of the data.
Here n = 11, which is odd.
Where n is the number of players.
∴ median = value of 1/2 (n + 1)th observation.
= 1/2 (11 + 1)
= 1/2 (12)
= 12/2
= 6
Then, the value of the 6th term = 15
Hence, the median is 15.
No, these three are not the same.
12. The weights (in kg.) of 15 students of a class are:
38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
(i) Find the mode and median of this data.
(ii) Is there more than one mode?
Answer:
Arranging the given weights of 15 students of a class in ascending order, we get
32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50
(i) Mode and Median
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 38 and 43 both occur 3 times.
Hence, the modes of the given weights are 38 and 43.
Median
The value of the middle-most observation is called the median of the data.
Here, n = 15, which is odd.
Where n is the number of students.
∴ median = value of 1/2 (n + 1)th observation
= 1/2 (15 + 1)
= 1/2 (16)
= 16/2
= 8
Then, the value of the 8th term = 40
Hence, the median is 40.
(ii) Yes, there are 2 modes for the given weights of the students.
13. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
Answer:
Arranging the given data in ascending order, we get
= 12, 12, 13, 13, 14, 14, 14, 16, 19
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 14 occurs the maximum number of times.
Hence, the mode of the given data is 14.
Median
The value of the middle-most observation is called the median of the data.
Here, n = 9, which is odd.
Where n is the number of students.
∴ median = value of 1/2 (9 + 1)th observation
= 1/2 (9 + 1)
= 1/2 (10)
= 10/2
= 5
Then, the value of the 5th term = 14
Hence, the median is 14.