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5.   Tell whether the statement is true or false:
        (i) The mode is always one of the numbers in a data.
        (ii) The mean is one of the numbers in a data.
       (iii) The median is always one of the numbers in a data.
       (iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

(i) True. Mode is the observation which occurs maximum number of times. Hence, Mode will always be the one of the numbers in a data. (ii) False. (iii) False. For even number of observations, the median is the mean of the  and values. (iv) Mean =  Hence, the statement is False.

4. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14

Given,  Arranging in ascending order =  We know, The mode is observation which occurs a maximum number of times. Median is the middle observation when that data is arranged in ascending or descending order. Now, Clearly,  occurs thrice. So,  is the mode of the data. Now, there are 9 values, so the median is the  Hence,  is the median value.

3. The weights (in kg.) of 15 students of a class are:
      38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
      (i) Find the mode and median of this data.
     (ii) Is there more than one mode?

Given, weights of 15 students (in kg)=  Arranging the data in ascending order =  (i) Clearly, 38 and 43 both occur thrice. So, they both are the mode of the data. Now, there are 15 values, so the median is the  Hence, 40 is the median value. (ii) Yes, there are two modes of the data given.

2. The runs scored in a cricket match by 11 players is as follows:
       6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
     Find the mean, mode and median of this data. Are the three same?

Runs scored in the match =  Arranging in ascending order =  Here, 15 occurs the maximum number of times. Hence, 15 is the mode of the data Now,     Therefore the mean score is  Now, the median is the middle observation of the data. There are 11 terms. Therefore the middle observation is  Therefore, 15 is the median of the data. No, they are not the same.  

1.  The scores in mathematics test (out of 25) of 15 students is as follows:
        19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20
       Find the mode and median of this data. Are they same?

Scores of 15 students are :  Arranging the data in ascending order =  We know, Mode: The number which occurs most frequently.  Median: Median is the mid-value of the set of numbers.  Here, 20 occurs 4 times, therefore 20 is the mode of the data. Also, the middle value is 20. Therefore, the median of the data is 20. Yes, the median and mode of this data are the same.
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