MEAN MEDIAN MODE FROM FREQUENCY TABLE

Problem 1 :

A class of 20 students all take a spelling test. Their results out of 10 are shown in the table.

Calculate :

a) Mean    b) Median   c)  Mode

Solution :

a) Mean :

= Total score / total number of students

Total score = 5(1) + 6(2) + 7(4) + 8(7) + 9(4) + 10(2)

= 5 + 12 + 28 + 56 + 36 + 20

= 157

Total number of students = 20

Mean = 157/20

= 7.85

b)  Median :

Total number of scores = 20

Median will be the average of 10^th and 11^th values. By observing the table, 10th value and 11th value will be 8.

Median = (8 + 8)/2

= 8

c) Mode :

Highest frequency of score is 8.

Mode = 8

Problem 2 :

A class of 30 students were asked how many pets they owned. The following data was obtained.

Calculate :

a) Mean    b) Median   c)  Mode

Solution :

a) Mean :

= Total number of pets / total number of students

Total number of pets = 0(4) + 1(12) + 2(11) + 3(3)

= 0 + 12 + 22 + 9

= 43

Total number of students = 30

Mean = 43/30

= 1.43

b)  Median :

Total number of scores = 20

Median will be the average of 15^th and 16^th values. By observing the table, 15^th value and 16^th value will be 1.

Median = (1 + 1)/2

= 1

c) Mode :

Highest frequency of score is 1.

Mode = 1

Problem 3 :

Sarah recorded the number of occupants in each car that drove down her street one day. The results are shown in the frequency columns graph.

a) Construct a frequency table from the graph.

b) How many cars did Sarah record data for ?

c) Find the 

i) Mean    ii) Median   iii) Mode

Solution :

a)

b) Number of cars recorded = 5 + 7 + 6 + 4 + 2

= 24 cars

c)  i) Mean :

= [1(5) + 2(7) + 3(6) + 4(4) + 5(2)]/24

= (5 + 14 + 18 + 16 + 10)/24

= 63/24

= 2.625

ii) Median :

Median = Average of 12th and 13th value

= (2 + 3)/2

= 5/2

= 2.5

iii)  Mode :

The highest frequency is 7.So, mode is 2.

Problem 4 :

50 people were asked how many times they had moved house. The results are given in the frequency table.

a) For this data, find the

i) Mean  ii) Median  iii) Mode

b) Construct a column graph for the data and show the position of the measures of of center on the horizontal axis.

Solution :

i) Mean :

Total number of house moves =

0(5) + 1(9) + 2(13) + 3(8) + 4(6) + 5(3) + 6(3) + 7(2) + 8(1)

= 0 + 9 + 26 + 24 + 24 + 15 + 18 + 14 + 8

= 138

Mean = 138 /50

= 2.76

ii) Median :

Median = Average of 25^th + 26^th values

= (2+2)/2

= 2

iii) Mode :

The highest frequency is 13 for the data 2. So, mode is 2.

b)