Mean Mode Median | Basics for GATE CS/IT

Mean means average.

Median means middle value in the list of number.

The “mode” is the value that occurs most often. If no number repeated then no mode exist.


Type 1 : Ungrouped Data

Que : Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

Solution :

Mean = Average , So Total sum divided by number of terms

Mean = (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Mode = Mode Frequent number , Here most occuring number is 13 .

So, Mode = 13

Median is middle value. First arrange given values in ascending order and then find the middle term(s).

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.

Note : If total number of terms is odd then middle term is (n+1)/2 but if total number of terms are even then you will get middle term as floating number say if you get 5.5 then take average of 5th and 6th number . (if 5th number is 6 and 7th number is 7 then your median will be (6+7)/2=6.5)


Type 2 : Grouped Data

Score 10-12 13-15 16-18 19-21 22-24
Frequency 4 6 13 9 8

Find Mean , Modal class and median class .

Solution

For mean find the middle value of each interval and multiply i.e with frequency to calculate total sum and then divide with total frequency.

Score 10-12
(Mid Value=11)
13-15
(Mid Value=14)
16-18
(Mid Value=17)
19-21
(Mid Value=20)
22-24
(Mid Value=23)
Frequency 4 6 13 9 8

Mean =  (11 × 4 + 14 × 6 + 17 × 13 + 20 × 9 + 23 × 8) ÷ 40

= (44 + 84 + 221 +180 + 184) ÷ 40

= 17.825

Modal Class = Interval with Max. Frequency

So here modal class = 16-18

Median Class : Class in which middle term lie i.e (40+1)/2 i.e 20.5

So here median class is 16-18


where:

  • L is the lower class boundary of the group containing the median
  • n is the total number of values
  • B is the cumulative frequency of the groups before the median group
  • G is the frequency of the median group
  • w is the group width

where:

  • L is the lower class boundary of the modal group
  • fm-1 is the frequency of the group before the modal group
  • fm is the frequency of the modal group
  • fm+1 is the frequency of the group after the modal group
  • w is the group width

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