Median And Mode

MEDIAN: If a set of numbers is arranged in order of size, the middle term is called the median. If there is an even number of terms, the median is the arithmetic mean of the two middle terms.

Examples

Find the median of a) 15, 11, 8, 21, 17, 3, 8         b) 3.8, 2.1, 4.4, 8.3, 9.2, 5.0.

Solution

a)Arrange the numbers in rank order (i.e from highest to lowest).

     21, 17, 15, 11, 8, 8, 3

There are seven numbers. The median is the 4^th number, 11 .

b)Arrange the numbers from the lowest to highest.

      2.1, 3.8, 4.4, 5.0, 8.3, 9.2

There are six numbers. The median is the mean of the 3^rd and 4^th terms.

     Median = (4.4 + 5.0) /2

                    = 4.7

MODE: The mode of a set of numbers is the number which appears most often, i.e. the number with the greatest frequency.

Example: Twenty-one students did an experiment to find the melting point of naphthalene. The table below shows their results. What was a) the modal temperature  b) the median temperature?

temperature (^oC)      78    79    80   81   82   83   90

frequency                   1      2       7     5      3     2      1

a)Seven students recorded a temperature of 80^oC. This was the most frequent result.

    Mode = 80^oC

b)There were 21 students. The median is the 11^th temperature. If the temperatures were written down in order, there would be one of 78^oC, two of 79^oC, seven of 80^oC, and so on. Since 1 +2 + 7 = 10, the 11^th temperature is one of the five 81^oCs.

     Median = 81^o C.

EVALUATION

1. For the following set of numbers:

13, 14, 14, 15, 18, 18, 19, 19, 19, 21

a)state the median, b) state the mode, c) calcilate the mean.

READING ASSIGNMENT

NGM BK 1 PG 196 – 203 Ex 18d nos 17 – 20

GENERAL EVALUATION

Prepare a frequency table for the following sets of data.

1)The shoe sizes of a group of 24 children are

    8    6    7    5    4    6    5    7

     6    5    7    6    8    5    4    6

     5    5    6    7    8    8    6    7

2)The ages of 32 students in Class 2 of a Junior Secondary School are

      11    12    11    12    12    14    14    13

      15    13    12    13    13    13    13    12

      14    14    13    15    14    11    12    14

      12    15    14    16    14    14    14    15

WEEKEND ASSIGNMENT

1. The number of goals scored by a team in nine handball matches are as follows:    3, 5, 7, 7, 8, 8, 8, 11, 15Which of the following statements are true of these scores?a)The mean is greater than the mode.b)The mode and the median are equal.c)The mean, median, and mode are all equal.

Use the table below to question 2-5

The table below shows the number of pupils (f) scoring a given mark (x) in attest.

X     2      3      4      5       6     7      8       9       10     11      12

f     3       8      7      10    13  16    15     15      6        2       5

• Find the mode.a)7       b) 8      c) 9      d) 10
• Find the median.a) 6       b) 7      c) 8      d) 9
• Calculate the mean.a) 6.7     b) 6.8     c) 6.9   d) 6.95
• Find the range.a)10        b) 11      c) 9      d) 12

THEORY

1. x, x, x, y represent four numbers. The mean of the numbers is 9,their median is 11. Find y
2. Students at a teacher training college are grouped by age as given in table below.

Age (years)       20       21       22      23      24      25

Frequency          4         5        10      16      12      3

1. Find the modal age.
2. Find the median age.
3. Calculate the mean age of the students.