**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:

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
- f
_{m-1}is the frequency of the group before the modal group - f
_{m}is the frequency of the modal group - f
_{m+1}is the frequency of the group after the modal group - w is the group width