Class IX Math NCERT Solution for Statistics 14.4

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.
Sol. To find mean:
        Here, n = 10,
        
        Thus, the median of the data = 3
        To find the mode:
        ∵ In the given data
              0 occurs 1 time, 1 occurs 1 time, 2 occurs 1 time, 3 occurs 4 times, 4 occurs 2 times, 
5 occurs 1 time
        ∵ 3 occurs maximum number of times.
        ∴ Mode = 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.
Sol. To find the mean:
        ∵ n = 15
        
        Thus, mean = 54.8
        To find median:
        Arranging the given data in an ascending order, we have
        39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
        ∵ n = 15, an odd number
        
        Thus, the median = 52
        To find mode:
        ∵ In the given data, the observation 52 occurs 3 times, i.e., the 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
Sol. Here, the given observations are in an ascending order.
        ∵ n = 10 (an even number of observations)
        
        ∴ x + 1 = 63 ⇒ x = 63 – 1 = 62
        Thus, the required value of x is 62.
4.   Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
Sol. Arranging the given data in an ascending order: 14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.
        ∴ The observation 14 is occurring the maximum number of times (i.e., 4 times)
        ∴ Mode of the given data = 14
5.   Find the mean salary of 60 workers of factory from the following table:
        
Sol. Let salaries be represented by xi and number of corresponding workers by fi.
        Note: The mean x of n observations having values as x1, x2, x3, ..., xn and occurring with
 frequencies f1, f2, f3, ...,
        fn respectively is given by
        
        Thus, the mean salary = ` 5080.33
        
        Thus, the required mean salary = ` 5080.33
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.
Sol. (i) Mean is a quantitative central tendency of a data.
               Example: For measuring central tendency of marks of a test we find the mean of the data.
        (ii) Median is a qualitative central tendency of a data.
               Example: For measuring central tendency of beauty of a group of women, we determine
 the median of the data.

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