MANAGEMENT FINANCE AND SCIENCE

Management Finance and Science

Management Finance and Science

Answer No. 1

Area

P

Q

Arithmetic mean

£ 190,000

£ 180,000

Mode

£ 210,000

£ 175,000

Median

£ 195,000

£ 190,000

Standard deviation

£ 10,000

£ 80,000

Sample size (number of houses)

100

144

(a)

The arithmetic mean is the sum of the values of the variable divided by the number of individuals. The mode is simply the most frequent value in a distribution, which characterized the greatest number of value. The median is the value of the data as it shows half of the data is below this value and half above. The median of a set of values is the value m such that the number of values in the set greater than or equal to m is the number of values m or less. Intuitively, we can say that the median is the midpoint of the data set, it divides into two halves. This is a position characteristic of the series. We can determine a median for a set of non-numeric values as far as we can choose a scheduling criterion values.

It may be interesting to know these three indicators that are mean, median and mode because together they already offer some clarification on a distribution. In particular, as the mean is pulled towards extreme values, we know that; if the average is much lower than the median, a few individual character values much lower than all others and if the average is much higher than the median, a few individuals character values much higher than all others

From the above table, it can be said that the average area of P is high as compared to area Q; the reason of this statement is that the average of area P is £ 10000 greater than area Q. Besides it, it is also observed that median value of area P is £ 195000 which is higher than the median value of area Q that is £ 190000. Furthermore, the area which occurs most often in the data set pertain to area P and Q are £ 210000 and £ 175000 respectively, which reflects that the average area of Q is lower in comparison to average area of P.

(b)

If the confidence limit is 90% then; the standard error of the average area of Q is:

Standard Error

=

Standard Deviation

=

80000

=

80000

=

6667

Sqrt (n)

Sqrt (144)

12

The critical value area Q is used to calculate the error margin. The value of critical region can be shown as a t- score which are expressed in the given steps;

Alpha (a): a = 1 - (confidence level / 100) = 0.05;

Significance level = p = 1 - a/2 = 1 - 0.1/2 = 0.95;

Degrees of freedom = df = n - 1 = 144 - 1 = 143

The cumulative probability is equal to 0.95 and the value of critical region is the t- score with 143 degrees of freedom; therefore, from the t-distribution, it is found that the critical value is 1.6556.

However, if the confidence limit is 95% then; the standard error of the average area of Q is:

Standard Error

=

Standard Deviation

=

80000

=

80000

=

6667

Sqrt ...