Part 2 (Numerical Descriptive Techniques)
31 43 56 23 49 42 33 61 44 28
48 38 44 35 40 64 52 42 47 39
53 27 36 35 20
x |
420 |
610 |
625 |
500 |
400 |
450 |
550 |
650 |
480 |
565 |
y |
2.80 |
3.60 |
3.75 |
3.00 |
2.50 |
2.70 |
3.50 |
3.90 |
2.95 |
3.30 |
14. A sample of eight observations of variables x and y is shown below. Enter the data on a sheet called Question 14.
x |
5 |
3 |
7 |
9 |
2 |
4 |
6 |
8 |
y |
20 |
23 |
15 |
11 |
27 |
21 |
17 |
14 |
a. Calculate the covariance and the coefficient of correlation, and comment on the relationship between x and y.
b. Draw the scatter diagram and plot the least squares line. Name this sheet Question 14 Scatter Diagram and make sure it follows the sheet called Question 14.
c. Estimate the value of y for x = 6.
Ordering the data from least to greatest, we get:
20 23 27 28 31 33 35 35 36 38 39 40 42 42 43 44 44 47 48 49 52 53 56 61 64
a) Median = ( N+1)/2 th data i.e 13th data t.e, 42
So, the median is 42 .
b)
So, the bottom half is
20 23 27 28 31 33 35 35 36 38 39 40
The median of these numbers is 34.
Q_{1}= 34
c)
The upper half is
42 43 44 44 47 48 49 52 53 56 61 64
The median of these numbers is 48.5.
Q_{3}= 48.5
d_)
Range = Maximum- Minimum = 64-20 = 44
Inter quartile range = Q_{3}- Q_{1} = 48.5 - 34 = 14.5
e)
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
Mean=Sum of terms/Number of terms
= 1030/ 25 = 41.2
f) Box plot
There is no outlier.
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