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## Chapter 14 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.

→ For mean:
Mean = Sum of all observation/Total number of observations
Mean = 2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3/10
Mean = 28/10
Mean = 2.8

→ For median:
To find median we have to arrange the given data into ascending or descending order. Therefore,
0, 1, 2, 3, 3, 3, 3, 4, 4, 5

Number of observations, n = 10 (which is even)
Therefore,
Median = [n/2]th observation + [n/2 + 1]th observation/2
Median = [10/2]th observation + [10/2 + 1]th observation/2
Median = 5th observation + 6th observation/2
Median = (3 + 3)/2
Median = 3

→ For mode:
To find mode, we have to arrange the given data into ascending or descending order. Therefore,
0, 1, 2, 3, 3, 3, 3, 4, 4, 5

After arranging the data, we see that 3 is mode of this data as it is occurring most frequently (4 times).

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.

→ For mean:
Mean = Sum of all observations/Total number of observations
Mean = 41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60/15
Mean = 822/10
Mean = 82.2

→ For median:
To find median, we have to arrange the given data in ascending or descending order. Therefore,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Number of observations, n = 15 (which is odd)
Therefore,
Median = [(n + 1)/2]th observation
Median = [15 + 1/2]th observation
Median = 8th observation or Median = 52

→ For mode:
To find mode we have to arrange the given data in ascending or descending order. Therefore,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

After arranging the data, we see that 52 is mode of this data as it is occurring most frequently (3 times).

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

To find the value of x, we have to first arrange the data in ascending order. Therefore,
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Number of observations = 10 (which is even)
Therefore,
Median = [n/2]th observation + [n/2 + 1]th observation/2
63 = [10/2]th observation + [10/2 + 1]th observation/2
63 = 5th observation + 6th observation/2
63 = (x + x + 2)/2
(63)2 = 2x + 2
126 = 2x + 2
124 = 2x
62 = x

Thus, the value of x is 62.

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

To find the mode, we have to first arrange the given data in ascending or descending order. Therefore,
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28

After arranging the data, we see that 14 is mode of this data as it is occurring most frequently (4 times).

Question 5: Find the mean salary of 60 workers of a factory from the following table:
 Salary (in ₹) Number of workers 3000 16 4000 12 5000 10 6000 8 7000 6 8000 4 9000 3 10000 1 Total 60

 Salary (in ₹) Number of workers (fi) fixi 3000 16 48000 4000 12 48000 5000 10 50000 6000 8 48000 7000 6 42000 8000 4 32000 9000 3 27000 10000 1 10000 Total: ∑fi = 60 ∑fixi = 305000 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 an appropriate measure of central tendency.

i) Mean marks obtained in an examination.
ii) Mean is not an appropriate measure of central tendency when all the terms of the data are not fairly close to each other. Let’s take an example, we have data of the form:
50, 51, 55, 54, 200

Mean of this data is equal to 82 which is not close to any of the terms present in the data. In such a case, median is a better method. Arranging data in the ascending order we get,
50, 51, 54, 55, 200

Clearly, median of this data is equal to 54 which is close to most of the terms present in the data.