Ex - 14.4
Question 1. The following number of goals was scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
Mode of data is the observation with the maximum frequency in data.
So, mode score of data is 3 as it is having maximum frequency as 4 in the data.
Find the mean, median and mode of this data.
(ii) The mean is not an appropriate measure of central tendency but the median is a appropriate measure of central tendency
Question 1. The following number of goals was scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
Solution
The number of goals scored by team is
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Arranging the number of goals in ascending order
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
As the number of observations is 10. 10 is an even number. So, median score will be
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
As the number of observations is 10. 10 is an even number. So, median score will be
Mode of data is the observation with the maximum frequency in data.
So, mode score of data is 3 as it is having maximum frequency as 4 in the data.
Question 2. In a mathematics test given to 15 students, the following marks (out of 100) are recorded:
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60Find the mean, median and mode of this data.
Solution
The marks of 15 students in mathematics test are
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Arranging the scores obtained by 15 students in an ascending order
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
As the number of observations is 15 that is odd so, median of data will be
= 8th observation while data is arranged in an ascending or descending order
So, median score of data = 52
Mode of data is the observation with the maximum frequency in data. So mode of this data is 52 having the highest frequency in data as 3.
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
As the number of observations is 15 that is odd so, median of data will be
= 8th observation while data is arranged in an ascending or descending orderSo, median score of data = 52
Mode of data is the observation with the maximum frequency in data. So mode of this data is 52 having the highest frequency in data as 3.
Question 3. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Solution
Total number of observation in the given data is 10 (even number). So median of this data will be mean of 
i.e. 5th and 
i.e. 6thobservations
i.e. 5th and i.e. 6thobservations
Question 4. Find the mode of
14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
Solution
Arranging the data in an ascending order
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here observation 14 is having the highest frequency i.e. 4 in given data. So, mode of given data is 14.
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here observation 14 is having the highest frequency i.e. 4 in given data. So, mode of given data is 14.
Question 5. Find the mean salary of 60 workers of a factory from the following table:
Salary (in Rs)
|
Number of workers
|
3000
|
16
|
4000
|
12
|
5000
|
10
|
6000
|
8
|
7000
|
6
|
8000
|
4
|
9000
|
3
|
1000
|
1
|
Total
|
60
|
Solution
As
Valaues of 
and 
can be computed
and can be computed
Salary (in Rs) (xi)
|
Number of workers (fi)
|
fixi
|
3000
|
16
|
3000 * 16 = 48000
|
4000
|
12
|
4000 * 12 = 48000
|
5000
|
10
|
5000 * 10 = 50000
|
6000
|
8
|
6000 * 8 = 48000
|
7000
|
6
|
7000 * 6 = 42000
|
8000
|
4
|
8000 * 4 = 32000
|
9000
|
3
|
9000 * 3 = 27000
|
10000
|
1
|
10000 * 1 = 10000
|
Total
|  |  |
So, mean salary of 60 workers is Rs 5083.33.
Question 6. Give one example of a situation in which
(i) The mean is an appropriate measure of central tendency.(ii) The mean is not an appropriate measure of central tendency but the median is a appropriate measure of central tendency
Solution
(i) Mean is appropriate measure of central tendency in all the cases where it is important to take all observations into account and data does not have any extreme values for example in case of temperature of a month
(ii) Mean is not suitable in cases where there are very high and low values for example salary in a company.
(ii) Mean is not suitable in cases where there are very high and low values for example salary in a company.
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