Mean, Median, Mode, and Range

Statistics                                                           name: Anna

WALT- Identify the mean, median and mode within a collection of data

Activity One

Answer the questions in a different colour

The definition of the mean in a statistical investigation is commonly referred to as the average. It is the total of all the data divided by the amount of data shown.

For example: if we have this range of data 3,5,7,1,2,3,6,8

3+5+7+1+2+3+6+5  = 32  = 4

             8                      8

1. Find the mean in this set of numbers

3,7,8,4,2,6,5,4,3,9 = 51 ➗ 10 = 5 r 1

2. Find the mean in the set of numbers

4,12,5,6,11,9,5 = 52 ➗ 7 = 7. r 3

3. Find the mean in this tally chart

Pets owned by students	Number of students
Dogs	IIIII IIIII
Cats	IIIII IIIII II
Fish	IIII
Rabbits	II

4. Find the mean in this set of numbers

24,12,16,18 = 70 ➗ 4 = 17.r 2

5. Find the mean in this set of numbers

5,9,12,4,10,7 = 47 ➗ 6 = 7. r 5

6. CHALLENGE QUESTION: Find the mean within this data, use the frequency table to help you

1,5,5,2,1,2,5,5,5,5,1,2,1,5,5 = 50 ➗ 15 = 3 r 5

Score	Frequency
1	4
2	3
5	8
Total	15

Activity Two

Answer the questions in a different colour

The definition of the median is the middle number within a set of numbers that have been put in order from size (biggest to smallest or smallest to biggest)

For example: 2,6,4,1,9 = 1,2,4,6,9 and the middle number is 4.

BUT say if there is more than one middle number… the median is found by taking the number midway between the middle pair of numbers:

3,6,1,4,9,2 = 1,2,3,4,6,9 → 3 + 4 = 3.5

                                             2

Find the median in these sets of numbers

1. 10,14,17,12,19,11,16 = 14

           10,11, 12, 14,16,17,19 = 14 is the middle number

2. 34,42,37,31,40  = 37

           31, 34, 37,40,42 = 37 is the middle number

3. 101, 167,138,124,198,149 = 143.5

            101, 124, 138,149, 167, 198 = 143.5  is the middle number

4. 54, 58,52,57,53,60 = 55.5

           52, 53, 54,57,58,60= 55.5 is the middle number

5. 1001, 1094, 1023, 1065, 1038, 1027, 1042 = 1038

           1001, 1023, 1027, 1038, 1042, 1065, 1094 = 1038 is the middle number

6. Find the median within this tally chart

Pets owned by students	Number of students
Dogs	IIIII IIIII
Cats	IIIII II
Fish	IIII
Rabbits	IIIII III
Hamsters	II

10, 12,4, 8, 2 = 8

2,4, 8, 10,12 = 8 is the middle number

Activity Three

The mode is the most frequent number in a set of data. The number that occurs most often.

For example: In a set of numbers 3, 7, 8, 4, 2, 6, 5, 4, 3, 9 there is two modes, 3 and 4 because they appear twice in the data set.

Note- There can either be 0, 1 or 2 modes. If there are 3 or more numbers occur the same number of times, there is no mode.

Find the mode in these sets of numbers

1. 2, 1, 5, 3, 7, 8, 5, 3 ,9 = 3 and 5
2. 1, 5, 3, 2, 9 ,4, 1, 6, 8, 0 = 1
3. 23, 45, 78, 12, 45, 67, 32, 46, 93, 12 = 12
4. 101, 121, 123, 145, 167, 121, 139, 145, 176 = 121
5. 394, 273, 219, 294, 183, 291, 273, 288, 271 = 273

RANGE:

1. 32, 41,37, 34, 40 = 41 - 32 = 9
2. 100, 92,96,94,98 = 100 - 92 = 8
3. 72, 79, 76,74,69,80 = 80 - 69 = 11
4. 54, 57, 52, 55, 58 = 58 - 52 = 6
5. 112, 125, 115, 111, 120 = 125 - 111 = 14