Question

IBL Company manager asked his statistic team to give to the production department the data on the number of phones manufactured over the 20 months.. The data collected are as follows:


Months
# of phones produced
1 2045
2 1566
3 9075
4 4563
5 5052
6 3465
7 2542
8 4134
9 3567
10 5163
11 4563
12 2453
13 462
14 2772
15 4263
16 5052
17 2846
18 5052
19 4130
20 5062




REQUIRED

PART A
1. Calculate the following using the data provided on the table:
a. the mean
b. median
c. mode
2. Find the Quartile 1 , Quartile 3 and inter-quartile of the phoines produced
3. Why is the inter-quartile calculated?
4. Describe the distribution of the data if Mean=Median = mode
5. How do we call data when Mode <Median <Mean and show with a diagram how such distribution looks?

Answer 1

Question 1

(A) Calculation of Mean,Median and Mode:

Mean = Sum of Observations / Number of observations

= {2045+1566+9075+4563+5052+3465+2542+4134+3567+5163+4563+2453+462+2772+4263+5052+2846+5052+4130+5062} / 20

= 77827/ 20

= 3891.35

Median :

We need to re arrange the data in ascending order which would be as follows:

462,1566,2045,2453,2542,2772,2846,3465,3567,4130,4134,4263,4563,4563,5052,5052,5052,5062,5163,9075

Since the number of observations (n) is an even number,

Median =  (n/2)th term + (n/2 +1)th term / 2

= (20/2/) th term + (20/2 +1)th term /2

= 10th gterm + 11 th term/ 2

= (4130+4134) /2

= 4132

Mode: It is the most repeated value in the data given ; Therefore Mode is  5052

Question 2

Calculation of Quartile 1 , Quartile 3 and Inter Quartile Range

We need to re arrange the data in ascending order which would be as follows:

462,1566,2045,2453,2542,2772,2846,3465,3567,4130,4134,4263,4563,4563,5052,5052,5052,5062,5163,9075

Quartile 1 = (n+1)/4 = 5.25th term

which means Q1 lies between 5th and 6 th term.

Hence we can take an average to find out the position of Q1 which is (2542+2772)/2 = 2657

Similarly Quartile 3 = 3* (n+1)/4 = 3* 5.25 = 15.75 th term

which means Q3 lies between15th and16 th term.

Hence we can take an average to find out the position of Q3 which is (5052+5052)/2= 5052

Inter Quartile Range = Q3 - Q1 = 5052-2657 = 2395

Question 3

Inter Quartile Range is calculated to find out where the most numbernof phonesmanufactured are placed in the given series of data. It basically represents the middle 50% percent of the data that ranges from 25th percentile to 75 th percentile.

If the Inter Quartile range is high , it means the data is more dispersed from the mean whereas when the Inter Quartile range is low, it means that the data points are more gathered towards the mean

Question 4

When the mean = Median = Mode, it is termed as symmetrical distribution of data. Normal distribution can be referred to as an example of Symmetric distribution. It is represented by a bell shaped curve where the distance of one side of the curve is exactly the same as the other side. The curve can be explained in the attached image

Question 5

When the values of mean, median and mode are not equal, it is termed as a skewed distribution. In a skewed distribution where Mode <Median <Mean , it is referred to as positively skewed distribution where we find that the right side of the curve is longer than the left side of the curve where the mean stands to the extreme right of the curve as it is of the greatest value. The curve can be explained in the attached image