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## Chapter 14: Statistics

TEXTBOOK’S 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. First of all we arrange the data in ascending order as follows:

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

Sum of the observations = 0 + 1 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 5 = 28

Here, the number of observations = 10 (even)

So, median

We see that the observations 3 occurs maximum number of times.

Hence, 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. We first arrange the data in ascending order as follows:

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Here, the number of observations = 15 (odd).

= value of 8th observations = 52

We see that 52 occurs a maximum number of times.

Hence, 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 number of observation = 10 (even)

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

Sol. We first arrange the data in ascending order.

14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28

We see that 14 occurs in the maximum number of times.

Hence, mode = 1

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

Sol. We prepare a table as follows:

Hence, mean salary = 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.

Sol. (i) If we find the meantime taken by an athlete in a race in which 10 athletes participate.

(ii) Collecting the data regarding the heights of people of a colony.