1. Measures of Central Tendency
Mean and Standard Deviation
for Ungrouped Data
Basic Statistics
Group 4
Ravisha Munjal
Pritesh Parikh
Aviral Mehrotra
Chandan Shukla
Akash Aggarwal
Sourav Roy

2. Measures of Central Tendency
Measures of central tendency are numerical descriptive measures which indicate or locate the center of a distribution or data set.
In layman’s term, a measure of central tendency is an AVERAGE. It is a single number of value which can be considered typical in a set of data as a whole. For example, in a class of 40 students, the average height would be the typical height of the members of this class as a whole.

3. MEAN
The MEAN of a set of values or measurements is the sum of all the measurements divided by the number of measurements in the set.
Among the three measures of central tendency, the mean is the most popular and widely used. It is sometimes called the arithmetic mean. If we compute the mean of the population, we call it the parametric or population mean, denoted by μ (read “mu”). If we get the mean of the sample, we call it the sample mean and it is denoted by (read “x bar”).

4. Mean for Ungrouped Data
For ungrouped or raw data, the mean has the following formula.
where = mean
= sum of the measurements or values
n = number of measurements

5. Ordinal Scale
This is used if the researcher wants to know the feelings or opinions of the respondents regarding any topic or issues of interest.
Next are examples of Ordinal scale questions. Respondents will choose the number which best represents their feeling regarding the statements. Note that the statements are grouped according to a theme.
Choices 5
(SA) Strongly Agree 4
(A) Agree 3
(N) Neutral 2
(D) Disagree 1
(SD) Strongly Disagree

6. Properties of Mean
Mean can be calculated for any set of numerical data, so it always exists.
A set of numerical data has one and only one mean.
Mean is the most reliable measure of central tendency since it takes into account every item in the set of data.
It is greatly affected by extreme or deviant values (outliers)
It is used only if the data are interval or ratio.

7. MODE
The MODE, denoted Mo, is the value which occurs most frequently in a set of measurements or values. In other words, it is the most popular value in a given set.
Examples:
Find the Mode.
The ages of five students are: 17, 18, 23, 20, and 19
The following are the descriptive evaluations of 5 teachers: VS, S, VS, VS, O
The grades of five students are : 4.0, 3.5, 4.0, 3.5, and 1.0
The weights of five boys in pounds are: 117, 218, 233, 120, and 117

8. Properties
It is used when you want to find the value which occurs most often.
It is a quick approximation of the average.
It is an inspection average.
It is the most unreliable among the three measures of central tendency because its value is undefined in some observations.

9. Satisfaction level of users with their current smart phone.
Majority of the users have a satisfaction level of 4 out of 5, on an average .
Mode is 4
Std. Deviation is 0.845

10. This chart shows the level of importance a user gives to a brand while purchasing a new smart phone.
Apple, Samsung and Xiaomi have the highest share in the smart phone segment in the particular order. Total share of these three companies is 50% of the market.

11. This chart shows the level of importance a user gives to the price of the new smart phone.
While buying a smart phone, most of the users give high level of importance to the price.

12. This chart shows the level of importance buyers give to design while purchasing a new smart phone.
Most of the users consider design of the smart phone an important factor.

13. The level of importance given to Screen Size is high.

14. Weight of the smart phone is not given very high attendance as in the case of other factors.

15. Mean of OS preference came out to be 4 which shows that people give high priority to OS.

16. Processing speed and camera quality scored the highest in preferences as there means came out to be 4.16 and 4.18 respectively.

17. Exchange offers have a mean of 2
Exchange offers have a mean of 2.54 which shows the mixed reactions towards this kind of offers from the customers.

18. Data analysis of customer review shows that people give relevant amount of importance to customer reviews.

20. Important Observations
Price, Processing speed and Camera quality are main features with mean score above 4.
Exchange offers are least important with a mean score of 2.54
Brand, design, consumer reviews and screen size are also important attributes which affect buying decision.
Weight of phone also play a role in buying decision with a mean score of 3.4

21. Interpretation
Samsung and Apple are two main market leaders holding 36.38% of the market share.
Motorola and Mi are emerging as new brands in the market.
First preference for buying a smartphone is Authorised dealer(1.89) followed by E-commerce(2.07) and Multi brand showroom(2.11)
Price, processor and camera quality are main features in driving the smartphone demand
Apple is a most used by all professionals

22. Managerial Implications
Average upgradation period of a smartphone is 3 years
As there is rapid change in technology, so, to enter the market our product must be unique.
Price
Features
Technology
Design
More authorized showroom should be introduced.
Price-range should be Rs.10,000-20,000