Statistics – Exercise 14.4 – (MATHEMATICS) – 9th Class

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Exercise 14.4

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.

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Sol. Arranging the data in ascending order, we get

0 , 1 , 2, 3, 3, 3, 3, 4, 4, 5

(i) Mean = {{0 + 1 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 5} \over {10}}

 = {{28} \over {10}} = 2.8

(ii) For median: n = 10.
Median is the mean of the values of observations at 5th and the 6th places.

∴   Median = {{3 + 3} \over 2} = 3

(iii) Mode: 3 occurs maximum number of times. Hence, mode is 3.


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.

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Sol.  Arranging the data in ascending order, we get
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

(i) Mean = {{39 + 40 + 40 + 41 + 42 + 46 + 48 + 52 + 52 + 52 + 60 + 62 + 96 + 98} \over {15}}

 = {{822} \over {15}} = 54.8

(ii) For median: n = 15, median is the value of the observation at the {{15 + 1} \over 2}th place, i.e., 8th place.

∴   Median = 52.

(iii) Mode: ’52’ occurs maximum number of times.

∴   Mode = 52.


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.

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Sol. Given observations: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.

Here n = 10, Median is mean of the values of the observations at {{10} \over 2}th, and  \left( {{{10} \over 2} + 1} \right)th i.e., 5th and 6th places.

∴  Median  = {{x + (x + 2)} \over 2} \Rightarrow {{2x + 2} \over 2} = 63

 \Rightarrow 2x = 126 - 2 = 124 \Rightarrow x = 62


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

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Sol. Arranging the data in ascending order, we have
14,     14,    14,    14,     17,     18,     18,     18,     22,     23,     25,    28
We notice 14 occurs maximum number of times.
Hence, the mode is 14.


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
700066
80004
90003
100001
Total60

 

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Sol.

Salary (in Rs.)(x)Number of workers (f)xf
30001648000
4000248000
50001050000
6000848000
7000642000
8000432000
9000327000
10000110000
∑f = 60∑xf = 305000

Mean = {{\sum {xf} } \over {\sum f }} = {{305000} \over {60}} = 5083.33

Hence, the mean salary is Rs. 5083.33


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.

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Sol. (i) Mean height of the students of a class.
(ii) Median weight of a pen, a book, a rubber band, a match box and a chair.


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