About Basics of Mean, Median, Mode. For Grade 7

1. Mean, Median, Mode
Narmatha Devi N
Statistics
Grade 7

2. Here, we will be seeing about basics of some common
measures of central tendencies : Mean, Median and Mode
About…

3. • Mean, Median mode are some measures of central tendency,
which can be used to study the various characteristics of a
given set of data.
• A measure of central tendency describes a set of data by
identifying the central position in the data set as a single value.
• It can be thought as a tendency of data to cluster around a
middle value.
Introduction

4. • The arithmetic mean of a given data is the sum of all
observations divided by the number of observations.
• It is also called as Average and is denoted by ҧ
𝑥
𝑨𝒓𝒊𝒕𝒉𝒎𝒓𝒕𝒊𝒄 𝒎𝒆𝒂𝒏 =
𝑺𝒖𝒎 𝒐𝒇 𝒂𝒍𝒍 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏𝒔
𝑵𝒐. 𝒐𝒇 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
Mean

5. • Date set : 51, 23, 42, 35, 42, 47
𝒎𝒆𝒂𝒏 =
𝑺𝒖𝒎 𝒐𝒇 𝒂𝒍𝒍 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏𝒔
𝑵𝒐.𝒐𝒇 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
=
51+23+42+35+42+47
6
=
240
6
Mean = 40
Mean - example

6. • The median is the middle value of a data set, which separates
the highest and lowest values equally.
• It is calculated by arranging the data set in ascending or
descending order the value in the exact middle.
𝑴𝒆𝒅𝒊𝒂𝒏 = 𝒎𝒊𝒅𝒅𝒍𝒆𝒎𝒐𝒔𝒕 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
Median

7. Step 1: Arrange the data in ascending or descending order.
Step 2: Find total number of observations, n.
Step 3:
if n is odd, 𝑚𝑒𝑑𝑖𝑎𝑛 =
𝑛+1
2
𝑡ℎ
𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
if n is even, 𝑚𝑒𝑑𝑖𝑎𝑛 =
(
𝑛
2
)𝑡ℎ𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛+ (
𝑛
2
+1)𝑡ℎ𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
2
Median - procedure

8. • Date set : 29, 12, 42, 53, 34
𝒎𝒆𝒅𝒊𝒂𝒏 = 𝒎𝒊𝒅𝒅𝒍𝒆𝒎𝒐𝒔𝒕 𝒗𝒂𝒍𝒖𝒆
Ascending order : 12, 29, 34, 42, 53
Middlemost value : 34
Median = 34
Median - example
• n = 5, odd
𝒎𝒆𝒅𝒊𝒂𝒏 =
𝑛 + 1
2
𝑡ℎ
𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
=
5+1
2
𝑡ℎ
𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
= 3 𝑡ℎ
𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
Median = 34

9. • Date set : 51, 23, 42, 36, 23, 47
𝒎𝒆𝒅𝒊𝒂𝒏 = 𝒎𝒊𝒅𝒅𝒍𝒆𝒎𝒐𝒔𝒕 𝒗𝒂𝒍𝒖𝒆
Ascending order : 23, 23, 36, 42, 47, 51
average - Middle value :
36+42
2
Median = 39
Median - example
• n = 6, even
𝒎𝒆𝒅𝒊𝒂𝒏 =
(
𝑛
2
)𝑡ℎ𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛+ (
𝑛
2
+1)𝑡ℎ𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
2
=
36+42
2
Median = 39

10. • The value which appears most often in the given data i.e. the
observation with the highest frequency is called a mode of
data.
• A data may have no mode, 1 mode, or more than 1 mode.
𝑴𝒐𝒅𝒆 = 𝒐𝒃𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏 𝒘𝒊𝒕𝒉 𝒎𝒂𝒙𝒊𝒎𝒖𝒎 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚
Mode

11. • Date set : 2, 9, 3, 12, 2, 4, 2, 5
𝒎𝒐𝒅𝒆 = 𝒎𝒐𝒔𝒕 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆
The observation 2 is repeated thrice
Mode = 2
Mode - example

12. ▪ The middlemost observation in a data set is called _______
▪ Arithmetic is also called as ________
▪ Find the mean, median, mode of data set { 8, 2, 5, 7, 3, 5 }
Testing time…

13. Thank You…