WORKSHEET ON MEAN MEDIAN MODE AND RANGE

Problem 1 :

In a survey of 10 households, the number of children was found to be

4, 1, 5, 4, 3, 7, 2, 3, 4, 1

(a) State the mode

(b) Calculate

(i) the mean number of children per household

(ii) the median number of children per household.

Problem 2 :

Eight people work in an office. They are paid hourly rates of

$12, $15, $15, $14, $13, $14, $13, $13

(a) Find

(i) the mean  (ii) the median  (iii) the mode.

(iv) What is the range?

Problem 3 :

Find the missing value 

7, 5, 10, x, 8 and 6

When the mean is 7.

Problem 4 :

Find the missing value

7, 2, x, 15, 20, 8, 14, 29

If the median is 13.

Problem 5 :

The mean of a sample of 6 numbers is 3.2. An extra value of 3.9 is included in the sample. What is the new mean?

Problem 6 :

The mean number of a set of 5 numbers is 12.7. What extra number must be added to bring the mean up to 13.1?

1. Solution :

(a)

4, 1, 5, 4, 3, 7, 2, 3, 4, 1

Mode  =  4 (most often repeated value)

(b) 

(i)  1 is repeated 2 times

2 is repeated 1 time

3 is repeated 2 times

4 is repeated 3 times

5 and 7is repeated once

Mean  =  (2(1) + 1(2)+2(3)+3(4)+5+7)/10

  =  34/10

  =  3.4

So, mean number of children is 3.4

(ii)  To find median, we arrange the given data in ascending order.

1, 1, 2, 3, 3, 4, 4, 4, 5, 7

Total number of terms  =  10 (Even)

Middle terms are  =  3 and 4

Average of 3 and 4  =  (3+4)/2

  =  3.5

Median is 3.5.

2. Solution :

(i)  Mean  =  [12(1) + 13(3) + 14(2) + 15(2)]/8

  =  13.5

So, the mean is 13.5

(ii)  To find median, let us arrange the given data is ascending order.

12, 13, 13, 13, 14, 14, 15, 15

Median  =  (13 + 14)/2

=  13.5

(iii)  Mode  =  13 (repeated three times)

(iv)  Range  =  Large value - small value

  =  15 - 12

Range =  3

3. Solution :

Mean  =  Average 

7  =  (7 + 5 + 10 + x + 8 + 6)/6

42  =  36 + x

x  =  42 - 36

x  =  6

4. Solution :

To find median, let us arrange the numerical value in ascending order by leaving the unknown.

2, 7, 8, 14, 15, 20, 29

Here number of terms is even, to find median, we will find the average of middle terms.

Let us consider the middle values as "a" and "b".

Median  =  (a + b)/2

13  =  (a+b)/2

26  =  a + b

One of the middle value is 14.

26  =  14 + b

b  =  12

So, the missing element is 12.

5. Solution :

Mena of 6 sample values  =  3.2.

Sum of 6 values / 6  =  3.2.

Sum of 6 values  =  3.2(6)

  =  19.2

One new value is included, that is 3.9

Sum of 7 sample values  =  19.2 + 3.9

  =  23.1

New mean  =  23.1/7

  =  3.3

6. Solution :

Mean of 5 numbers  =  12.7

Sum of 5 number / 5  =  12.7

Sum of 5 numbers  =  12.7(5)

=  63.5

Let x be the new value to be added.

new mean  =  13.1

Sum of 6 values / 6  =  13.1

(63.5 + x)/6  =  13.1

63.5 + x  =  13.1(6)

63.5 + x  =  78.6

x  =  91.7- 63.5

x  =  15.1

So, the new value to be added is 15.1

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