Statistics

Exercise 14.4

Question 1. The following number of goals were 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.

Answer: Mean = (Sum of observations)/(Number of observations)
`= (2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3)/10`

`= 28/10 = 2.8`

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, 60
Find the mean, median and mode of this data.

Answer: Mean = (Sum of observations)/(Number of observations)
`= (39 + 40 + 40 + 41 + 42 + 46 + 48 + 52 + 52 + 52 + 54 + 60 + 62 + 96 + 98)/15`

`= 792/15 = 52.8`

As there are odd number of observations so,
Median `= (n + 1)/2 = (15 + 1)/2 =` 8th term = 52
Mode = The term with most frequency = 52


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

Answer: Mean `= 63 = (29 + 32 + 48 + 50 + x + x + 2 + 72 + 78 + 84 + 95)/10`

Or, `630 = 490 + 2x`
Or, `2x = 630 – 490 = 140`
Or, `x = 70`

Question 4: Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Answer: Mode = term with most frequency = 14


Question 5: Find the mean salary of 60 workers of a factory from the following table:

Salary (in Rs.)Number of workers
300016
400012
500010
60008
70006
80004
90003
100001
Total60

Answer:

Salary (in Rs.)(xi)No. of workers (fi)fixi
30001648000
40001248000
50001050000
6000848000
7000642000
8000432000
9000327000
10000110000
Total`Σf_i = 60``Σf_i\x_i = 305000`

`Me\an\=(Σf_i\x_i)/(Σf_i)=305000/60=5083.33`

Question 6: Give one example of a situation in which

(i) the mean is an appropriate measure of central tendency.

Answer: When data does not have extreme values then mean is an appropriate measure of central tendency.

(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency

Answer: When data has extreme values then median is an appropriate measure of central tendency.



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