**Statistics**

**Question 1.The following number of goals were scored by a team in a series of 10 matches2, 3, 4, 5, 0, 1, 3, 3, 4, 3.Find the mean, median and mode of these scores.**

**Solution:**

To find the mean :

Here, n = 10

Thus, mean = 2.8

To find median:

Now arranging the given data in ascending order,

we have 0,1, 2, 3, 3, 3, 3, 4, 4, 5

∵ n = 10, an even number

Thus, median = 3

To find mode:

In the given data, the observation 3 occurs 4 times,

i.e., maximum number of times.

Thus, mode = 3

**Question 2.In a mathematics test given to 15 students, the following marks (out of 100) are recorded41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60Find the mean, median and mode of this data.**

**Solution:**

To find the mean:

Here, n = 15

Thus, mean = 54.8

To find median:

Arranging the given data in 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, median = 52

To find mode:

In the given data, the observation 52 occurs 3 times,

i.e., the maximum number of times.

Thus, mode = 52

**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**

**Solution:**

Here, the given observations are in ascending order.

Since, n = 10 (an even number)

Since, median = 63 [Given]

∵ x + 1 = 63 ⇒ x = 63 – 1 = 62

Thus, the required value of x is 62.

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

**Solution:**

Arranging the given data in ascending order, we have 14, 14, 14, 14, 17, 18, 18, 18, 22, 23 25, 28.

Since the observation 14 is occuring the maximum number of times (i.e. 4 times)

∴ Mode of the given data = 14

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

**Solution:**

Thus, the required mean salary = Rs. 5083.33

**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.**

**Solution:**

(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.